Question

A textile company produces two types of materials A and B. The material A is produced according to direct orders from furniture manufacturers. The material B is distributed to retail fabric stores. The average production rates for the material A and B are identical at 1,000 meters/hour. By running two shifts the operational capacity of the plant is 80 hours per week.

The marketing department reports that the maximum estimated sales for the following week is 70,000 meters of material A and 45,000 metres of material B. According to the accounting department, the profit from a metre of material A is SAR 2.50 and from a metre of material B is RSAR. 1.50.

The management of the company decides that a stable employment level is a primary' goal for the firm. Therefore, whenever there is demand exceeding normal production capacity, the management simply expands production capacity' by providing overtime. However, management feels that overtime operation of the plant of more than 10 hours per week should be avoided because of the accelerating costs. The management has the following goals in the order of importance:

1) The first goal into avoid any underutilization of production capacity (i.e., to maintain stable employment at normal capacity).

2) The second goal is to limit the overtime operation of the plant to 10 hours.

3) The third goal is to achieve the sales goals of 70,000 metres of material A and 45,000

metres of material B.

4) The last goal is to minimize the overtime operation of the plant as much as possible.

Formulate this as a goal programming problem to help the management for the best decision. Solve the problem using Graphical Method and Simplex Method.

Answer 1