Exam 9: Linear Programming

Which of the choices below constitutes a simultaneous solution to these equations? (1)3x + 4y = 10 and (2)5x + 4y = 14

The logistics/operations manager of a mail order house purchases two products for resale: King Beds (K)and Queen Beds (Q).Each King Bed costs $500 and requires 100 cubic feet of storage space,and each Queen Bed costs $300 and requires 90 cubic feet of storage space.The manager has $75,000 to invest in beds this week,and her warehouse has 18,000 cubic feet available for storage.Profit for each King Bed is $300,and for each Queen Bed is $150.Which of the following is not a feasible purchase combination?

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Columbia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.What is the Dominican bean constraint?

The logistics/operations manager of a mail order house purchases two products for resale: King Beds (K)and Queen Beds (Q).Each King Bed costs $500 and requires 100 cubic feet of storage space,and each Queen Bed costs $300 and requires 90 cubic feet of storage space.The manager has $75,000 to invest in beds this week,and her warehouse has 18,000 cubic feet available for storage.Profit for each King Bed is $300,and for each Queen Bed is $150.What is the objective function?

The term "range of feasibility" refers to coefficients of the objective function.

Which of the following is not a necessary assumption in order for a linear programming model to be used effectively?

The feasible solution space only contains points that satisfy all constraints.

Every constraint in a maximization problem has a slack variable.

Which objective function has the same slope as this one: $4x + $2y = $20?

Consider the graphical linear programming problem below: Maximize Z = $15X + $20y Subject to: (i)8x + 5y $\le$ 40 (ii).4x + y $\ge$ 4 Solve the values of x and y that will maximize revenue.What revenue will result?

A company produces two products (A and B)using three resources (I,II,and III).Each product A requires 1 unit of resource I and 3 units of resource II; and has a profit of $1.Each product B requires 2 units of resource I,3 units of resource II,and 4 units of resource III; and has a profit of $3.Resource I is constrained to 40 units maximum per day; resource II,90 units; and resource III,60 units.What is the optimum production combination and its profits?

A shadow price reflects which of the following in a maximization problem?

A company produces two products (A and B)using three resources (I,II,and III).Each product A requires 1 unit of resource I and 3 units of resource II; and has a profit of $1.Each product B requires 2 units of resource I,3 units of resource II,and 4 units of resource III; and has a profit of $3.Resource I is constrained to 40 units maximum per day; resource II,90 units; and resource III,60 units.What is the slack (unused amount)for each resource for the optimum production combination?

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R)and sassafras soda (S).Two resources are constrained: production time (T),of which she has at most 12 hours per day; and carbonated water (W),of which she can get at most 1500 gallons per day.A case of root beer requires 2 minutes of time and 5 gallons of water to produce,while a case of sassafras soda requires 3 minutes of time and 5 gallons of water.Profits for the root beer are $6.00 per case,and profits for the sassafras soda are $4.00 per case.For the production combination of 180 Root beer and 0 Sassafras sodas,which resource is "slack" (not fully used)?

A local bagel shop produces two products: bagels (B)and croissants (C).Each bagel requires 6 ounces of flour,1 gram of yeast,and 2 tablespoons of sugar.A croissant requires 3 ounces of flour,1 gram of yeast,and 4 tablespoons of sugar.The company has 6,600 ounces of flour,1,400 grams of yeast,and 4,800 tablespoons of sugar available for today's production run.Bagel profits are 20 cents each,and croissant profits are 30 cents each.Using the graphical method,what are optimal profits for today's production run?

The region which satisfies all of the constraints in linear programming is called the:

Every change in the value of an objective function coefficient will lead to a changed optimal solution.

The owner of Crackers,Inc.produces two kinds of crackers: Deluxe (D)and Classic (C).She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour,and 2,000 ounces of salt.A box of Deluxe crackers requires 2 ounces of sugar,6 ounces of flour,and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar,8 ounces of flour,and 2 ounces of salt.Profits for a box of Deluxe crackers are $0.40; and for a box of Classic crackers,$0.50.Using the graphical method,what are profits for the optimal production combination?

The feasible solution space is the set of all feasible combinations of decision variables as defined by only binding constraints.

The owner of Crackers,Inc.produces two kinds of crackers: Deluxe (D)and Classic (C).She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour,and 2,000 ounces of salt.A box of Deluxe crackers requires 2 ounces of sugar,6 ounces of flour,and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar,8 ounces of flour,and 2 ounces of salt.Profits for a box of Deluxe crackers are $0.40; and for a box of Classic crackers,$0.50.What is the constraint for sugar?