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Exam 3: Linear Programming: a Geometric Approach

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Write a system of linear inequalities that describes the shaded region. Write a system of linear inequalities that describes the shaded region.

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Question 161

Soundex produces two models of clock radios. Model A requires 15 min of work on assembly line I and 10 min of work on assembly line II. Model B requires 9 min of work on assembly line I and 12 min of work on assembly line II. At most 25 hr of assembly time on line I and 21 hr of assembly time on line II are available each day. Soundex anticipates a profit of $12 on model A and $10 on model B. Because of previous overproduction, management decides to limit the production of model A clock radios to no more than 80/day. The range of values that the contribution to the profit of a model A clock radio can assume without changing the optimal solution is Soundex produces two models of clock radios. Model A requires 15 min of work on assembly line I and 10 min of work on assembly line II. Model B requires 9 min of work on assembly line I and 12 min of work on assembly line II. At most 25 hr of assembly time on line I and 21 hr of assembly time on line II are available each day. Soundex anticipates a profit of $12 on model A and $10 on model B. Because of previous overproduction, management decides to limit the production of model A clock radios to no more than 80/day. The range of values that the contribution to the profit of a model A clock radio can assume without changing the optimal solution is . If the contribution to the profit of a model A clock radio is changed to $9.50/radio, will the original optimal solution still hold? Answer yes or no. __________ ​ What will be the optimal profit? Round to the nearest dollar. $ __________ . If the contribution to the profit of a model A clock radio is changed to $9.50/radio, will the original optimal solution still hold? Answer yes or no. __________ ​ What will be the optimal profit? Round to the nearest dollar. $ __________

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Question 162

Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Objective function Subject to Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Constrained 1 Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Constrained 2 Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . But the line with equation Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . is parallel to the line Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Thus, the coordinates of the point are found by solving the system of linear equations Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . The solutions are Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . and Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . The nonnegativity of x implies that Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Next, the nonnegativity of y implies that Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Thus, h must satisfy the inequalities Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . and Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . The resulting profit is calculated as follows: Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Upon setting h = 1, we find Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . type-A souvenirs and Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . type-B souvenirs, where Consider the production problem: One company wishes to produce two types of souvenirs: type A and type B. Each type-A souvenir will result in a profit of $1, and each type-B souvenir will result in a profit of $1.2. To manufacture a type-A souvenir requires 2 minutes on machine I and 1 minute on machine II. A type-B souvenir requires 1 minute on machine I and 3 minutes on machine II.There are 180 minutes available on machine I and 300 minutes available on machine II for processing the order. Maximaze Objective function Subject to Constrained 1 Constrained 2 Now suppose the time available on machine I is changed from 180 minutes to (180 + h) minutes, where h is a real number. Then the constraint on machine I is changed to But the line with equation is parallel to the line associated with the original constraint 1. As you can see from the figure , the result of adding the constant h to the right-hand side of constraint 1 is to shift the current optimal solution from the point C to the new optimal solution occurring at the point C. To find the coordinates of C, we observe that C is the point of intersection of the lines with equations Thus, the coordinates of the point are found by solving the system of linear equations The solutions are and The nonnegativity of x implies that Next, the nonnegativity of y implies that Thus, h must satisfy the inequalities . Computations reveal that for a meaningful solution the time available for machine I must range between (180 - 80) and (180 + 420) minutes-that is, between 100 and 600 minutes. According to the problem, optimal solution would be and The resulting profit is calculated as follows: Upon setting h = 1, we find Since the optimal profit for the original problem is $159.6, we see that the shadow price for the first resource is 149.16 - 148.80, or $.36. Show that if the time available on machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for machine I, then company profit is maximized by producing type-A souvenirs and type-B souvenirs, where . .

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Question 163

National Business Machines manufactures two models of fax machines: A and B. Each model A costs $58 to make, and each model B costs $150. The profits are $37 for each model A and $60 for each model B fax machine. The total number of fax machines demanded per month does not exceed 2,700 and the company has earmarked no more than $740,000/month for manufacturing costs. How many units of each model should National make each month in order to maximize its monthly profits? National Business Machines manufactures two models of fax machines: A and B. Each model A costs $58 to make, and each model B costs $150. The profits are $37 for each model A and $60 for each model B fax machine. The total number of fax machines demanded per month does not exceed 2,700 and the company has earmarked no more than $740,000/month for manufacturing costs. How many units of each model should National make each month in order to maximize its monthly profits? __________ __________ What is the optimal profit? $ __________ __________ National Business Machines manufactures two models of fax machines: A and B. Each model A costs $58 to make, and each model B costs $150. The profits are $37 for each model A and $60 for each model B fax machine. The total number of fax machines demanded per month does not exceed 2,700 and the company has earmarked no more than $740,000/month for manufacturing costs. How many units of each model should National make each month in order to maximize its monthly profits? __________ __________ What is the optimal profit? $ __________ __________ What is the optimal profit? National Business Machines manufactures two models of fax machines: A and B. Each model A costs $58 to make, and each model B costs $150. The profits are $37 for each model A and $60 for each model B fax machine. The total number of fax machines demanded per month does not exceed 2,700 and the company has earmarked no more than $740,000/month for manufacturing costs. How many units of each model should National make each month in order to maximize its monthly profits? __________ __________ What is the optimal profit? $ __________ $ __________

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Question 164

Write a system of linear inequalities that describes the shaded region. ​ Write a system of linear inequalities that describes the shaded region. ​ ​ Answer or . ​ ​ Answer Write a system of linear inequalities that describes the shaded region. ​ ​ Answer or . ​ or Write a system of linear inequalities that describes the shaded region. ​ ​ Answer or . ​ . ​ Write a system of linear inequalities that describes the shaded region. ​ ​ Answer or . ​

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Question 165

You are given a linear programming problem. Use the method of corners to solve the problem. Maximize You are given a linear programming problem. Use the method of corners to solve the problem. Maximize = __________ = __________ = __________ Find the range of values that the coefficient of x can assume without changing the optimal solution. ≤ c ≤ Find the range of values that resource 1 can assume. ≤ b ≤ Find the shadow price for resource 1. Express your answer to two decimal places, if necessary. $ __________ Identify the binding and nonbinding constraints. Constraint 1 is __________ Constraint 2 is __________ Constraint 3 is __________ You are given a linear programming problem. Use the method of corners to solve the problem. Maximize = __________ = __________ = __________ Find the range of values that the coefficient of x can assume without changing the optimal solution. ≤ c ≤ Find the range of values that resource 1 can assume. ≤ b ≤ Find the shadow price for resource 1. Express your answer to two decimal places, if necessary. $ __________ Identify the binding and nonbinding constraints. Constraint 1 is __________ Constraint 2 is __________ Constraint 3 is __________ You are given a linear programming problem. Use the method of corners to solve the problem. Maximize = __________ = __________ = __________ Find the range of values that the coefficient of x can assume without changing the optimal solution. ≤ c ≤ Find the range of values that resource 1 can assume. ≤ b ≤ Find the shadow price for resource 1. Express your answer to two decimal places, if necessary. $ __________ Identify the binding and nonbinding constraints. Constraint 1 is __________ Constraint 2 is __________ Constraint 3 is __________ = __________ You are given a linear programming problem. Use the method of corners to solve the problem. Maximize = __________ = __________ = __________ Find the range of values that the coefficient of x can assume without changing the optimal solution. ≤ c ≤ Find the range of values that resource 1 can assume. ≤ b ≤ Find the shadow price for resource 1. Express your answer to two decimal places, if necessary. $ __________ Identify the binding and nonbinding constraints. Constraint 1 is __________ Constraint 2 is __________ Constraint 3 is __________ = __________ You are given a linear programming problem. Use the method of corners to solve the problem. Maximize = __________ = __________ = __________ Find the range of values that the coefficient of x can assume without changing the optimal solution. ≤ c ≤ Find the range of values that resource 1 can assume. ≤ b ≤ Find the shadow price for resource 1. Express your answer to two decimal places, if necessary. $ __________ Identify the binding and nonbinding constraints. Constraint 1 is __________ Constraint 2 is __________ Constraint 3 is __________ = __________ Find the range of values that the coefficient of x can assume without changing the optimal solution. ≤ c ≤ Find the range of values that resource 1 can assume. ≤ b ≤ Find the shadow price for resource 1. Express your answer to two decimal places, if necessary. $ __________ Identify the binding and nonbinding constraints. Constraint 1 is __________ Constraint 2 is __________ Constraint 3 is __________

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Question 166

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded.

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Question 167

Solve the linear programming problem by the method of corners. Solve the linear programming problem by the method of corners. x = __________; y = __________; P = __________ x = __________; y = __________; P = __________

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Question 168

Solve the linear programming problem by the method of corners. Maximize Solve the linear programming problem by the method of corners. Maximize subject to subject to Solve the linear programming problem by the method of corners. Maximize subject to Solve the linear programming problem by the method of corners. Maximize subject to Solve the linear programming problem by the method of corners. Maximize subject to Solve the linear programming problem by the method of corners. Maximize subject to

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Question 169

Find the optimal (maximum and minimum) values of the objective function on the feasible set S. If no maximum or minimum value exists, enter no. ​ Find the optimal (maximum and minimum) values of the objective function on the feasible set S. If no maximum or minimum value exists, enter no. ​ ​ ​ __________, __________ ​ Find the optimal (maximum and minimum) values of the objective function on the feasible set S. If no maximum or minimum value exists, enter no. ​ ​ ​ __________, __________ ​ Find the optimal (maximum and minimum) values of the objective function on the feasible set S. If no maximum or minimum value exists, enter no. ​ ​ ​ __________, __________ __________, Find the optimal (maximum and minimum) values of the objective function on the feasible set S. If no maximum or minimum value exists, enter no. ​ ​ ​ __________, __________ __________

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Question 170

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded.

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Question 171

Find the graphical solution of the inequality. Find the graphical solution of the inequality.

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Question 172

Find the graphical solution of the inequality. ​ Find the graphical solution of the inequality. ​ ​ ​

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Question 173

Soundex produces two models of clock radios. Model A requires 15 min of work on assembly line I and 10 min of work on assembly line II. Model B requires 12 min of work on assembly line I and 20 min of work on assembly line II. At most 21 hr of assembly time on line I and 19 hr of assembly time on line II are available each day. Soundex anticipates a profit of $12 on model A and $10 on model B. Because of previous overproduction, management decides to limit the production of model A clock radios to no more than 80/day. ​ Find the range of values that the resource associated with the time constraint on machine I can assume. Find the shadow price for the resource associated with the time constraint on machine I. Round your answer to the nearest cent. ​

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Question 174

Formulate but do not solve the following exercise as a linear programming problem. A financier plans to invest up to $5 million in three projects. She estimates that project A will yield a return of 11% on her investment, project B will yield a return of 16% on her investment, and project C will yield a return of 23% on her investment. Because of the risks associated with the investments, she decided to put not more than 40% of her total investment in project C. She also decided that her investments in projects B and C should not exceed 70% of her total investment. Finally, she decided that her investment in project A should be at least 70% of her investments in projects B and C. How much should the financier invest in each project if she wishes to maximize the total returns on her investments?

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Question 175

A finance company has a total of $25 million earmarked for homeowner and auto loans. On the average, homeowner loans have a 8% annual rate of return, whereas auto loans yield a 12% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans. Determine the total amount of loans of each type the company should extend to each category in order to maximize its returns. $ __________ million in homeowner loans, $ __________ million in auto loans What are the optimal returns? (Round your answer to the nearest hundredth, if necessary). $ __________ million

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Question 176

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​ Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​ ​ ​

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Question 177

Solve the linear programming problem by the method of corners. Solve the linear programming problem by the method of corners. x = __________; y = __________; P = __________ x = __________; y = __________; P = __________

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Question 178

Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​ Determine graphically the solution set for the system of inequalities and indicate whether the solution set is bounded or unbounded. ​ ​ ​

(Multiple Choice)
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Question 179

Solve the following linear programming problem by the method of corners. Solve the following linear programming problem by the method of corners. __________ __________ __________ Solve the following linear programming problem by the method of corners. __________ __________ __________ __________ Solve the following linear programming problem by the method of corners. __________ __________ __________ __________ Solve the following linear programming problem by the method of corners. __________ __________ __________ __________

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Question 180
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