# Linear Programming and Sensitivity Analysis

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. For the production combination of 135 regular cases and 0 diet cases, which resource is completely used up (at capacity)?

a. only time

b. only syrup

c. time and syrup

d. neither time nor syrup

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. If the Mallory Furniture company decides to purchase 150 big shelves and no medium shelves, which of the two resources will be left over?

a. investment money only

b. storage space only

c. investment money and storage space

d. neither investment money nor storage space

Given the following linear programming problem:

Max Z = 15x + 20y

Subject to (1) 8x + 5y 40

(2) 4x + y 4

What is the maximum revenue at the optimal solution?

a. $120

b. $160

c. $185

d. $200

Given the following linear programming problem:

Min Z = 2x + 8y

Subject to (1) 8x + 4y 64

(2) 2x + 4y 32

(3) y 2

Determine the optimum values for x and y.

a. x = 2; y = 6

b. x = 6; y = 2

c. x = 12; y = 2

d. x = 2; y = 2

e. x = 6; y = 5

Which of the following could not be a linear programming problem constraint?

a. 3A + 21B > -2

b. 12A + 9B 3

c. 2A + 4B = 3

d. 4A + 7B + 2C + 9D 5

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#### Solution Summary

The explanation to the linear program and sensitivity analysis is provided.

Linear Programming Sensitivity Analysis

PLEASE EXPLAIN YOUR ANSWERS (why did you choose T instead of F or A instead of C, etc.).

C 1. Which of the following is not a component of the structure of a linear programming model?

a. parameters

b. decision variables

c. environment of certainty

d. constraints

F 2. In a linear programming model, the number of constraints must be less than the number of decision variables.

B 3. The theoretical limit on the number of constraints that can be handled by a linear programming problem is

a. 2

b. 3

c. 4

d. Unlimited

A 4. If the feasible region for linear programming problem is unbounded, then the solution to the corresponding linear programming problem is _______ unbounded.

a. always

b. sometimes

c. never

d. rarely