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Exam 6: B: Process Design and Facility Layout

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Question 21

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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?

A) $10,000
B) $4,600
C) $2,500
D) $5,200
E) $6,400

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

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Question 22

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?

A) 0 A & 0 B
B) 0 A & 400 B
C) 200 A & 300 B
D) 400 A & 0 B
E) 400 A & 400 B

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

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Question 23

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

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 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?

A shadow price reflects which of the following in a maximization problem?

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?

In linear programming,sensitivity analysis is associated with: I.objective function coefficient. II.right-hand side values of constraints. III.constraint coefficient.

Wood Specialties Company produces wall shelves,bookends,and shadow boxes.It is necessary to plan the production schedule for next week.The wall shelves,bookends,and shadow boxes are made of oak,of which the company has 600 board feet.A wall shelf requires 4 board feet,bookends require 2 board feet,and a shadow box requires 3 board feet.The company has a power saw for cutting the oak boards into the appropriate pieces; a wall shelf requires 30 minutes,bookends require 15 minutes,and a shadow box requires 15 minutes.The power saw is expected to be available for 36 hours next week.After cutting,the pieces of work in process are hand finished in the finishing department,which consists of 4 skilled and experienced craftsmen,each of whom can complete any of the products.A wall shelf requires 60 minutes of finishing,bookends require 30 minutes,and a shadow box requires 90 minutes.The finishing department is expected to operate for 40 hours next week.Wall shelves sell for $29.95 and have a unit variable cost of $17.95; bookends sell for $11.95 and have a unit variable cost of $4.95; a shadow box sells for $16.95 and has a unit variable cost of $8.95. (i)Is this a problem in maximization or minimization? (ii)What are the decision variables? Suggest symbols for them. (iii)What is the objective function? (iv)What are the constraints?

The equation 3xy = 9 is linear.

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?

A small firm makes three products,which all follow the same three step process,which consists of milling,inspection,and drilling.Product A requires 6 minutes of milling,5 minutes of inspection,and 4 minutes of drilling; product B requires 2.5 minutes of milling,2 minutes of inspection,and 2 minutes of drilling; and product C requires 5 minutes of milling,4 minutes of inspection,and 8 minutes of drilling.The department has 20 hours available during the next period for milling,15 hours for inspection,and 24 hours for drilling.Product A contributes $6.00 per unit to profit,product B contributes $4.00 per unit,and product C contributes $10.00 per unit.Determine the optimum mix of products in terms of maximizing contributions to profits for the next period.

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.

For the products A,B,C,and D,which of the following could be a linear programming objective function?

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?

A maximization problem may be characterized by all greater than or equal to constraints.

Consider the linear programming problem below: Minimize Z = $2x + $8y Subject to: (i)8x + 4y³ 64 (ii)2x + 4y³ 32 (iii)y³ 2 Determine the optimum amounts of x and y in terms of cost minimization.What is the minimum cost?

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?

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

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?