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Exam 19: Linear Programming

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Question 51

Multiple Choice

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An analyst, having solved a linear programming problem, determined that he had 10 more units of resource Q than previously believed. Upon modifying his program, he observed that the list of basic variables did not change, but the value of the objective function increased by $30. This means that resource's Q's shadow price was

A) $1.50.
B) $3.00.
C) $6.00.
D) $15.00.
E) $30.00.

F) A) and B)
G) A) and C)

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Question 52

Multiple Choice

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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 is the production time constraint (in minutes) ?

A) 2 R + 3 S ≤ 720
B) 2 R + 5 S ≤ 720
C) 3 R + 2 S ≤ 720
D) 3 R + 5 S ≤ 720
E) 5 R + 5 S ≤ 720

F) B) and E)
G) C) and E)

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Question 53

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?

The operations manager for the Blue Moon Brewing Co. produces two beers: Lite (L) and Dark (D) . Two of his resources are constrained: production time, which is limited to 8 hours (480 minutes) per day; and malt extract (one of his ingredients) , of which he can get only 675 gallons each day. To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract, while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract. Profits for Lite beer are $3.00 per keg, and profits for Dark beer are $2.00 per keg. For the production combination of 135 Lite and 0 Dark, which resource is slack (not fully used) ?

A change in the value of an objective function coefficient does not change the optimal solution.

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 Columbia bean constraint?

The theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem is

In graphical linear programming to maximize profit, the objective function is: (I) a family of parallel lines.(II) a family of isoprofit lines.(III) interpolated.(IV) linear.

Which of the following choices constitutes a simultaneous solution to these equations?

When a change in the value of an objective function coefficient remains within the range of optimality, the optimal solution also remains the same.

Which of the following could not be a linear programming problem constraint?

An electronics firm produces two models of pocket calculators: the A-100 (A) , which is an inexpensive four-function calculator, and the B-200 (B) , which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. What is the assembly time constraint (in hours) ?

A linear programming problem can have multiple optimal solutions.

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?

An electronics firm produces two models of pocket calculators: the A-100 (A) , which is an inexpensive four-function calculator, and the B-200 (B) , which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100s this week and a maximum of 1,000 B-200s. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each. What is the objective function?

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

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. What is the sugar constraint (in tablespoons) ?

LP problems must have a single goal or objective specified.