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Exam 19: Linear Programming

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Question 41

True/False

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Using the enumeration approach, optimality is obtained by evaluating every coordinate.

A) True
B) False

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Question 42

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It has been determined that, with respect to resource X, a one-unit increase in availability of X is within the range of feasibility for X and would lead to a $3.50 increase in the value of the objective function. This $3.50 value would be X's

A) range of optimality.
B) shadow price.
C) range of feasibility.
D) slack.
E) surplus.

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

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Question 43

Multiple Choice

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

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. What is the time constraint?

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

In linear programming, a nonzero reduced cost is associated with a

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. What are optimal daily profits?

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?

What combination of x and y will yield the optimum for this problem?

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?

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

The value of an objective function always decreases as it is moved away from the origin.

The term isoprofit line means that all points on the line will yield the same profit.

The term range of feasibility refers to a constraint's right-hand-side quantity.

The equation 5 x + 7 y = 10 is linear.

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) ?

_________________ is a means of assessing the impact of changing parameters in a linear programming model.

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

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. For the production combination of 180 root beer and 0 sassafras soda, which resource is slack (not fully used) ?