Question: A local company manufactures three products, A1, A2, and A3. The maximum forecasted demand for these products are; 55,000, 135,000 and 195,000 units per month, respectively. The company is planning to manufacture at least 12,500, 38,500, and 52,000 units per month, respectively, to fulfill contractual agreements with its several major customers. Contributions (profit exclusive of direct labor costs) are $18.60, $13.80, and $10.75 per unit, respectively. Each unit must go through four manufacturing stages. Pending expected expansion, the current daily production capacity is 280, 460, 510, and 325 hours per shift for stages 1, 2, 3, and 4, respectively. There are 20 working days, 2 shifts per day (early shift and late shift), in the month. The number of production hours required to process 1,000 units of each product through each stage is given in Table1. The cost per hour of operating the stages is given in Table 2.

Table 1 Table 2

Stage A1 A2 A3 Early Shift Late Shift

1 30 60 30 $2.25 $3.20

2 180 160 75 6.00 9.60

3 260 80 45 10.50 15.25

4 55 40 80 8.10 12.00

In order to reduce the risk, the profit for each product must be at least 22% of the total profit and the profit for product A1 cannot be more than 46% of total the profit.

Formulate a linear programming model to determine the optimal production quantities for product A1, A2, and A3.

Use LINDO or WINQSB to solve this problem.

Interpret your computer printout.