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Exam 9: Linear Programming

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Question 1

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The simplex method is an LP algorithm that can solve problems having more than two decision variables.

A) True
B) False

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Question 2

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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 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.What is the objective function?

A) Z = $4 R + $6 S
B) Z = $2 R + $3 S
C) Z = $6 R + $4 S
D) Z = $3 R + $2 S
E) Z = $5 R + $5 S

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

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Question 3

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The equation 3xy = 9 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 $0.40; and for a box of Classic crackers,$0.50.Which of the following is not a feasible production combination?

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.What are optimal weekly profits?

For a nonbinding constraint,if the left side is greater than the right side,we say that there is surplus; if the left side is smaller than the right side,we say that there is slack.

What is the linear programming approach where substituting the coordinates of each corner point into the objective function determines the corner point which is optimal?

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.What is the production time constraint (in minutes) ?

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

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

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.Is the production combination 10 A's and 10 B's feasible?

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?

An objective function represents a family of parallel lines.

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A) and British (B) .Two of his resources are constrained: Colombia 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 Colombian bean constraint?

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 objective function?

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?

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 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.Is the production combination 15 A's and 15 B's feasible?

An example of a decision variable in an LP problem is profit maximization.

What combination of x and y will yield the optimum solution for this problem? Maximize Z = $3x + $15y; Subject to: (1) 2x + 4y $\le$ 12 (2) 5x + 2y $\le$ 10