# linear programming

The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. The company operates one "8 hour" shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup is limited to maximum production capacity of 675 gallons per day. Production of a regular case requires 2 minutes and 5 gallons of syrup, while production of 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 optimal daily profit?

a. $220

b. $270

c. $320

d. $420

e. $520

Mallory 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 $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the objective function?

a. Z = $300B + $150M

b. Z = $300M + $150B

c. Z = $300B + $500M

d. Z = $500B + $300M

Mallory 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. What is the storage space constraint?

a. 90B + 100M 18000

b. 100B + 90M ≤ 18000

c. 90B + 100M 18000

c. 500B + 300M 18000

d. 300B + 500M 18000

Mallory 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. What is the weekly maximum profit?

a. $25000

b. $35000

c. $45000

d. $55000

e. $65000

For a linear programming problem, assume that a given resource has not been fully used. In other words, the slack value associated with the resource constraint is positive. We can conclude that the shadow price associated with that constraint:

a. will have a positive value

b. will have a negative value

c. will have a value of zero

d. could have a positive, negative or a value of zero. (no sign restrictions)

For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from

3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. 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. If the production manager decides to produce of 0 bottles of light beer and 400 bottles of dark beer, it will result in slack of

a. malt only

b. wheat only

c. both malt and wheat

d. neither malt nor wheat

Mallory 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. Which of the following is not a feasible purchase combination?

a. 0 big shelves and 200 medium shelves

b. 0 big shelves and 0 medium shelves

c. 150 big shelves and 0 medium shelves

d. 100 big shelves and 100 medium shelves

#### Solution Summary

Explanations on various quantitive analysis