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Exam 9: Linear Programming

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Question 41

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Linear programming techniques will produce an optimal solution to problems that involve limitations on resources.

A) True
B) False

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Question 42

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

A) 0 L & 0 D
B) 0 L & 120 D
C) 90 L & 75 D
D) 135 L & 0 D
E) 135 L & 120 D

F) C) and D)
G) A) and E)

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Question 43

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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 constraint for resource I?

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

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.

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

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 constraint for resource III?

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.Using the graphical method,what are optimal daily profits?

Which graphical solution method finds the optimal corner point by sliding the objective function line (which is an isocost line) toward the origin instead of away from it?

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

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.For the production combination of 600 bagels and 800 croissants,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.Which of the following is not a feasible production combination?

Which of the choices below constitutes a simultaneous solution to these equations? (1) 3x + 2y = 6 and (2) 6x + 3y = 12

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-100's this week and a maximum of 1,000 B-200's.Profits for the A-100 are $1.00 each,and profits for the B-200 are $4.00 each.For the production combination of 1,400 A-100's and 900 B-200's,which resource is "slack" (not fully used) ?

Constraints limit the alternatives available to a decision-maker.

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

The term "range of optimality" refers to a range of values for an objective function coefficient over which the optimal solution values of the decision variables remain the same.

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-100's this week and a maximum of 1,000 B-200's.Profits for the A-100 are $1.00 each,and profits for the B-200 are $4.00 each.Which of the following is not a feasible production/sales combination?

LP problems must have a single goal or objective specified.

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?