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Exam 6: B: Process Design and Facility Layout

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Question 51

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

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Question 52

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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.Using the graphical method,what are profits for the optimal production combination?

A) $800
B) $500
C) $640
D) $620
E) $600

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

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Question 53

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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: 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?

Every constraint in a maximization problem has a slack variable.

What combination of x and y will provide a minimum for this problem? Minimize Z = $3x + $15y; Subject to: (1) 2x + 4y > 12 (2) 5x + 2y > 10

Which of the choices below constitutes a simultaneous solution to these equations? (1) 3x + 4y = 10 and (2) 5x + 4y = 14

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

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

Constraints limit the alternatives available to a decision-maker.

The feasible solution space only contains points that satisfy all constraints.

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.For the production combination of 0 American and 400 British,which resource is "slack" (not fully used) ?

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?

A constraint that does not form a unique boundary of the feasible solution space is a:

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.What is the sugar constraint (in tablespoons) ?

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.For the production combination of 180 Root beer and 0 Sassafras sodas,which resource is "slack" (not fully used) ?

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 objective function?

A manager must decide on the mix of products to produce for the coming week.Product A requires three minutes per unit for molding,two minutes per unit for painting,and one minute per unit for packing.Product B requires two minutes per unit for molding,four minutes per unit for painting,and three minutes per unit for packing.There will be 600 minutes available for molding,600 minutes for painting,and 420 minutes for packing.Both products have profits of $1.50 per unit. (i)What combination of A and B will maximize profit? (ii)What is the maximum possible profit? (iii)How much of each resource will be unused for your solution?

The simplex method is an LP algorithm that can be used for solving only large-scale problems.

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?