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Exam 25: Linear Programming

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Question 1

True/False

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An objective function represents a family of parallel lines.

A) True
B) False

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Question 2

Multiple Choice

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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. Which of the following is not a feasible production combination?

A) 0 A and 0 B
B) 0 A and 400 B
C) 200 A and 300 B
D) 400 A and 0 B
E) 400 A and 400 B

F) A) and B)
G) B) and E)

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Question 3

Multiple Choice

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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. For the purchase combination 0 king beds and 200 queen beds, which resource is slack (not fully used) ?

Linear programming techniques will always produce an optimal solution to an LP problem.

In graphical linear programming, when the objective function is parallel to one of the binding constraints, then:

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 a constraint's right-hand-side quantity.

Which of the following choices constitutes a simultaneous solution to these equations? 3x+2y= 6 6x+3y=12

Constraints limit the alternatives available to a decision maker

Once we go beyond two decision variables, typically the ___________ method of linear programming must be used.

A constraint that does not form a unique boundary of the feasible solution space is a:

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 storage space 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. Which of the following is not a feasible purchase 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 1,500 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. What are optimal daily profits?

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 $.40; and for a box of Classic crackers, $.50. For the production combination of 800 boxes of Deluxe and 600 boxes of Classic, which resource is slack (not fully used) ?

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 maximum profit?

A redundant constraint is one that:

A shadow price indicates how much a one-unit decrease/increase in the right-hand-side value of a constraint will decrease/increase the optimal value of the objective function.

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 are optimal weekly profits?

Which of the following choices constitutes a simultaneous solution to these equations? 3x+4y=10 5x+4y=14