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Exam 6: B: Process Design and Facility Layout

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Question 1

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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 slack (unused amount)for each resource for the optimum production combination?

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S(I)= 0;
S...

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Question 2

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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.What is the objective function?

A) Z = $1 A + $2 B
B) Z = $12 A + $8 B
C) Z = $2 A + $1 B
D) Z = $8 A + $12 B
E) Z = $4 A + $8 B

F) All of the above
G) C) and E)

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C

Question 3

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If a single optimal solution exists to a graphical LP problem,it will exist at a corner point.

Which of the following is not written in the standard form of a linear programming problem constraint?

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

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?

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

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

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.Using the graphical method,what are optimal profits for today's production run?

Which of the following is not a necessary assumption in order for a linear programming model to be used effectively?

A linear programming problem can have multiple optimal solutions.

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

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) ?

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.What is the constraint for sugar?

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 removal of a redundant constraint does not affect the feasible solution space.

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?

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.

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