Management Science

DISCUSSION 3

1. The Xecko Tool Company

The Xecko Tool Company is considering bidding on a job for two airplane wing parts. Each wing part must be processed through three manufacturing stages: stamping, drilling, and finishing for which the company has limited available hours. The linear programming model to determine how many of part 1 (x1) and part 2 (x2) the company should produce in order to maximize its profit is as follows:

maximize Z = $650x1 + 910x2

subject to

4x1 + 7.5x2 ≤ 105 (stamping, hr.)

6.2x1 + 4.9x2 ≤ 90 (drilling, hr.)

9.1x1 + 4.1x2 ≤ 110 (finishing, hr.)

x1, x2≥ 0

A. Solve the model graphically.

B. Indicate how much slack resource is available at the optimal solution point.

C. Solve this model by using Excel.

D. What is the Dual Problem?

2. The N. Dustrious Company

The N. Dustrious Company produces two products: I and II. The raw material

requirements, space needed for storage, production rates, and selling prices for these

products are given in Table 1.

The total amount of raw material available per day for both products is 1575 1b. The total storage space for all products is 1500 ft2, and a maximum of 7 hours per day can be used for production. The company wants to determine how many units of each product to produce per day to maximize its total income.

A. Formulate the LP problem

B. Solve graphically

C. Solve this model by using Excel.

D. What is the Dual Problem?

3. A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows.

Hours/Unit

Product Line 1 Line 2

A 12 4

B 4 8

Total hours 60 40

a. Formulate a linear programming model to determine the optimal product mix that will

maximize profit.

b. Transform this model into standard...