In a linear programming problem, a valid objective function can be represented as

a. Max Z = 5xy

b. Max Z 5×2 + 2y2

c. Max 3x + 3y + 1/3z

d. Min (x1 + x2) / x3

A plant manager is attempting to determine the production schedule of various products to maximize profit. Assume that a machine hour constraint is binding. If the original amount of machine hours available is 200 minutes., and the rangeof feasibility is from 130 minutes to 340 minutes, providing two additional machine hours will result in the:

a. same product mix, different total profit

b. different product mix, same total profit as before

c. same product mix, same total profit

d. different product mix, different total profit

The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. Which of the following is not a feasible solution?

a. 0 L and 0 D

b. 0 L and 400 D

c. 200 L and 300 D

d. 400 L and 400 D

The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?

a. 2R + 4D 480

b. 2D + 4R 480

c. 2R + 3D 480

d. 3R + 2D 480

e. 3R + 4D 480

A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today’s production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the optimal daily profit?

a. $380

b. $400

c. $420

d. $440

e. $480

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.

a. x21 + x22 8000

b. x12 + x22 8000

c. x11 + x12 8000

d. x21 + x22 8000

e. x11 + x12 8000

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the demand constraint for gasoline type 1.

a. x21 + x22 =11000

b. x12 + x22 =11000

c. x11 + x21 11000

d. x11 + x21 = 11000

e. x11 + x12 11000

Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. In order to maximize profit, how many big shelves (B) and how many medium shelves (M) should be purchased?

a. B = 90, M = 75

b. B = 135, M = 15

c. B = 150, M = 0

d. B = 0, M = 200

e. B = 100, M = 100