Question 1

Consider the linear programming problem. ​  
Sketch the feasible set for the linear programming problem.

Accepted Answer

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B)    
C)    
D)    
E)    
A)    
B)    
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D)    
E)

Question 2

A financier plans to invest up to $7 million in three projects. She estimates that project A will yield a return of 5% on her investment, project B will yield a return of 10% on her investment, and project C will yield a return of 20% on her investment. Because of the risks associated with the investments, she decided to put not more than 20% of her total investment in project C. She also decided that her investments in projects B and C should not exceed 60% of her total investment. Finally, she decided that her investment in project A should be at least 60% of her total investment. How much should the financier invest in each project if she wishes to maximize the total returns on her investments? What is the maximum amount she can expect to make from her investments? ​

Accepted Answer

A)  Project A: $1,350,000, project B: $1,350,000, and project C: $2,900,000; maximum profit: $690000 
B)  Project A: $2,850,000, project B: $2,900,000, and project C: $1,350,000; maximum profit: $230,000 
C)  Project A: $1,400,000, project B: $2,800,000, and project C:$2,800,000; maximum profit: $910,000 
D)  Project A: $2,800,000, project B: $2,800,000, and project C: $1,400,000; maximum profit: $700,000 
A)  Project A: $1,350,000, project B: $1,350,000, and project C: $2,900,000; maximum profit: $690000 
B)  Project A: $2,850,000, project B: $2,900,000, and project C: $1,350,000; maximum profit: $230,000 
C)  Project A: $1,400,000, project B: $2,800,000, and project C:$2,800,000; maximum profit: $910,000 
D)  Project A: $2,800,000, project B: $2,800,000, and project C: $1,400,000; maximum profit: $700,000

Question 3

A company manufactures products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for departments I, II, and III are 990, 1,010, and 870, respectively. The time requirements (in hours/unit) and the profit per unit for each product are as follows:   If management decides that the number of units of product B manufactured must equal or exceed the number of units of products A and C manufactured, how many units of each product should the company produce in order to maximize its profit?
__________ units A
__________ units B
__________ units C
Maximum profit is $ __________.

Accepted Answer

The answer of A company manufactures products A, B, and...

Question 4

Rewrite the given linear programming problem as a maximization problem with constraints involving inequalities of the form   (with the exception of the inequalities   ).

Accepted Answer

A)  Maximize  
Subject to         
B)  Maximize  
Subject to        
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C)  Maximize  
Subject to        
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D)  Maximize  
Subject to        
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A)  Maximize  
Subject to         
B)  Maximize  
Subject to        
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C)  Maximize  
Subject to        
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D)  Maximize  
Subject to        
​

Question 5

A farmer has 150 acres of land suitable for cultivating crops A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $7,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 3,300 labor-hours available. If he expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should he plant in order to maximize his profit? What is the largest profit the farmer can realize? Are there any resources left over?

Accepted Answer

A)  65 acres of crop A, 80 acres of crop B; maximum profit $25750; $0 left over, 5 acres of land left over, 0 labor-hours left over 
B)  150 acres of crop A, 80 acres of crop B; maximum profit $51,000; $2,200 left over, 0 acres of land left over, 0 labor-hours left over 
C)  90 acres of crop A, 60 acres of crop B; maximum profit $51,000; $200 left over, 0 acres of land left over, 0 labor-hours left over 
D)  150 acres of crop A, 0 acres of crop B; maximum profit $22,500; $2,200 left over, 0 acres of land left over, 300 labor-hours left over 
A)  65 acres of crop A, 80 acres of crop B; maximum profit $25750; $0 left over, 5 acres of land left over, 0 labor-hours left over 
B)  150 acres of crop A, 80 acres of crop B; maximum profit $51,000; $2,200 left over, 0 acres of land left over, 0 labor-hours left over 
C)  90 acres of crop A, 60 acres of crop B; maximum profit $51,000; $200 left over, 0 acres of land left over, 0 labor-hours left over 
D)  150 acres of crop A, 0 acres of crop B; maximum profit $22,500; $2,200 left over, 0 acres of land left over, 300 labor-hours left over

Question 6

Use the simplex method for solving nonstandard problems to solve the given linear programming problem.

Accepted Answer

A)    34 
B)    34 
C)    34 
D)    34 
E)    34 
A)    34 
B)    34 
C)    34 
D)    34 
E)    34

Question 7

Use the Simplex Method for Solving Nonstandard Problems to solve the linear programming problem.

Accepted Answer

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B)    
C)    
D)    
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D)    
E)

Question 8

Wayland Company manufacturers two models of its twin size futons, standard and deluxe, in two locations, I and II. The maximum output at location I is 600/week, whereas the maximum output at location II is 400/week. The profit per futon for standard and deluxe models manufactured at Location I is $30 and $20 respectively; the profit per futon for standard and deluxe modelsmanufatured at Location II is $34 and $18, respectively. For a certain week, the company has recieved an order of 600 standard models and 300 deluxe models. If prior commitments dictate that the number of deluxe models manufactured at Location II not exceed the number of standard models manufactured there by more than 50. Find how many of each model should be manufactured at each location so as to satisfy the order and at the same time maximize the Wayland's profit. What is the maximum profit?

Accepted Answer

A)  400 standard and 300 deluxe futons should be produced at location I and 400 standard and 0 deluxe futons should be produced at location II for a maximum profit of $25,600. 
B)  200 standard and 0 deluxe futons should be produced at location I and 400 standard and 300 deluxe futons should be produced at location II for a maximum profit of $25,600. 
C)  200 standard and 0 deluxe futons should be produced at location I and 40.0 standard and 300 deluxe futons should be produced at location II for a maximum profit of $25,600. 
D)  200 standard and 300 deluxe futons should be produced at location I and 400 standard and 0 deluxe futons should be produced at location II for a maximum profit of $25,600. 
E)  400 standard and 300 deluxe futons should be produced at location I and 200 standard and 0 deluxe futons should be produced at location II for a maximum profit of $25,600. 
A)  400 standard and 300 deluxe futons should be produced at location I and 400 standard and 0 deluxe futons should be produced at location II for a maximum profit of $25,600. 
B)  200 standard and 0 deluxe futons should be produced at location I and 400 standard and 300 deluxe futons should be produced at location II for a maximum profit of $25,600. 
C)  200 standard and 0 deluxe futons should be produced at location I and 40.0 standard and 300 deluxe futons should be produced at location II for a maximum profit of $25,600. 
D)  200 standard and 300 deluxe futons should be produced at location I and 400 standard and 0 deluxe futons should be produced at location II for a maximum profit of $25,600. 
E)  400 standard and 300 deluxe futons should be produced at location I and 200 standard and 0 deluxe futons should be produced at location II for a maximum profit of $25,600.

Question 9

Solve the given minimization problem by the simplex method.

Accepted Answer

The answer of Solve the given minimization problem by the...

Question 10

Use the simplex method for solving nonstandard problems to solve the given linear programming problem.   
 x = __________
y = __________
z = __________
C = __________

Accepted Answer

The answer of Use the simplex method for solving nonstandard...

Question 11

Solve the primal problem.

Accepted Answer

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E)

Question 12

Solve the linear programming problem by the simplex method. Minimize   subject to

Accepted Answer

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B)    
C)    
D)    
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D)

Question 13

Use the Simplex Method for Solving Nonstandard Problems to solve the linear programming problem.

Accepted Answer

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Question 14

The owner of the Health JuiceBar wishes to prepare a low-calorie fruit juice with a high vitamin A and vitamin C content by blending orange juice and pink grapefruit juice. Each glass of the blended juice is to contain at least 1,610 International Units (IU) of vitamin A and 194 IU of vitamin C. One ounce of orange juice contains 70 IU of vitamin A, 14 IU of vitamin C, and 13 calories; each ounce of pink grapefruit juice contains 140 IU of vitamin A, 12 IU of vitamin C, and 12 calories. How many ounces of each juice should a glass of the blend contain if it is to meet the minimum vitamin requirements while containing a minimum number of calories?
__________ ounces of orange juice
__________ ounces of pink grapefruit juice
__________ calories

Accepted Answer

The answer of The owner of the Health JuiceBar wishes...

Question 15

Maximize   subject to 3x + 10y + 4z ≤ 120
5x + 3y + 8z ≤ 9
8x + 10y + 3z ≤ 104
X ≥ 0, y ≥ 0, z ≥ 0

Accepted Answer

A)  x = 0, y = 0, z = 0, u = 92, v = 0, w = 74, P = 3 
B)  x = 0, y = 0, z = 0, u = 92, v = 0, w = 76, P = 15 
C)  x = 0, y = 0, z = 3, u = 90, v = 0, w = 76, P = 3 
D)  x = 0, y = 3, z = 0, u = 90, v = 0, w = 74, P = 21 
E)  x = 0, y = 3, z = 0, u = 90, v = 0, w = 74, P = 15 
A)  x = 0, y = 0, z = 0, u = 92, v = 0, w = 74, P = 3 
B)  x = 0, y = 0, z = 0, u = 92, v = 0, w = 76, P = 15 
C)  x = 0, y = 0, z = 3, u = 90, v = 0, w = 76, P = 3 
D)  x = 0, y = 3, z = 0, u = 90, v = 0, w = 74, P = 21 
E)  x = 0, y = 3, z = 0, u = 90, v = 0, w = 74, P = 15

Question 16

Solve the linear programming problem by the simplex method.

Accepted Answer

A)  x = 13, y = 4, z = 0, u = 73, v = 0, w = 0, P = 129 
B)  x = 4, y = 0, z = 13, u = 73, v = 0, w = 0, P = 250 
C)  x = 0, y = 13, z = 0, u = 73, v = 0, w = 0, P = 134 
D)  x = 0, y = 0, z = 4, u = 73, v = 0, w = 0, P = 76 
A)  x = 13, y = 4, z = 0, u = 73, v = 0, w = 0, P = 129 
B)  x = 4, y = 0, z = 13, u = 73, v = 0, w = 0, P = 250 
C)  x = 0, y = 13, z = 0, u = 73, v = 0, w = 0, P = 134 
D)  x = 0, y = 0, z = 4, u = 73, v = 0, w = 0, P = 76

Question 17

Consider the linear programming problem. Maximize     subject to       Sketch the feasible set for the linear programming problem.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
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E)

Question 18

A pharmaceutical company produces three kinds of cold formulas: I, II, and III. It takes 2 hr to produce 1,000 bottles of formula I, 4 hr to produce 1,000 bottles of formula II, and 3 hr to produce 1,000 bottles of formula III. The profits for each 1,000 bottles of formula I, formula II, and formula III are $220, $130, and $190, respectively. Suppose, for a certain production run, there are enough ingredients on hand to make at most 7,000 bottles of formula I, 17,000 bottles of formula II, and 9,000 bottles of formula III. Furthermore, suppose the time for the production run is limited to a maximum of 100 hr. How many bottles of each formula should be produced in this production run so that the profit is maximized?
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__________ bottles of formula I,
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__________ bottles of formula II,
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__________ bottles of formula III
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What is the maximum profit realizable by the company? $ __________
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Are there any resources left over?
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ingredients for __________ bottles of formula I,
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ingredients for __________ bottles of formula II,
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ingredients for __________ bottles of formula III,
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__________ hr of the time for the production run

Accepted Answer

@#IMG-DLM& ; @#IMG-DLM& ; @#IMG-DLM& ; @#IMG-DLM&

Question 19

Use the simplex method for solving nonstandard problems to solve the given linear programming problem.   
 x = __________
y = __________
z = __________
C = __________

Accepted Answer

The answer of Use the simplex method for solving nonstandard...

Question 20

Use the technique developed in this section to solve the minimization problem.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Consider the linear programming problem. Sketch the feasible set for the linear programming problem.

Rewrite the given linear programming problem as a maximization problem with constraints involving inequalities of the form (with the exception of the inequalities ).

Use the simplex method for solving nonstandard problems to solve the given linear programming problem.

Use the Simplex Method for Solving Nonstandard Problems to solve the linear programming problem.

Solve the given minimization problem by the simplex method.

Use the simplex method for solving nonstandard problems to solve the given linear programming problem. x = y = z = C =

Solve the primal problem.

Solve the linear programming problem by the simplex method. Minimize subject to

Use the Simplex Method for Solving Nonstandard Problems to solve the linear programming problem.

Maximize subject to 3x + 10y + 4z ≤ 120 5x + 3y + 8z ≤ 9 8x + 10y + 3z ≤ 104 X ≥ 0, y ≥ 0, z ≥ 0

Solve the linear programming problem by the simplex method.

Consider the linear programming problem. Maximize subject to Sketch the feasible set for the linear programming problem.

Use the simplex method for solving nonstandard problems to solve the given linear programming problem. x = y = z = C =

Use the technique developed in this section to solve the minimization problem.

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

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Exam 4: Linear Programming: an Algebraic Approach

Consider the linear programming problem. ​ Sketch the feasible set for the linear programming problem.

Rewrite the given linear programming problem as a maximization problem with constraints involving inequalities of the form (with the exception of the inequalities ).

Use the simplex method for solving nonstandard problems to solve the given linear programming problem.

Use the Simplex Method for Solving Nonstandard Problems to solve the linear programming problem.

Solve the given minimization problem by the simplex method.

Use the simplex method for solving nonstandard problems to solve the given linear programming problem. x = __________ y = __________ z = __________ C = __________

Solve the primal problem.

Solve the linear programming problem by the simplex method. Minimize subject to

Use the Simplex Method for Solving Nonstandard Problems to solve the linear programming problem.

Maximize subject to 3x + 10y + 4z ≤ 120 5x + 3y + 8z ≤ 9 8x + 10y + 3z ≤ 104 X ≥ 0, y ≥ 0, z ≥ 0

Solve the linear programming problem by the simplex method.

Consider the linear programming problem. Maximize subject to Sketch the feasible set for the linear programming problem.

Use the simplex method for solving nonstandard problems to solve the given linear programming problem. x = __________ y = __________ z = __________ C = __________

Use the technique developed in this section to solve the minimization problem.

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Consider the linear programming problem. Sketch the feasible set for the linear programming problem.

Use the simplex method for solving nonstandard problems to solve the given linear programming problem. x = y = z = C =

Use the simplex method for solving nonstandard problems to solve the given linear programming problem. x = y = z = C =