A production scheduler must develop an aggregate plan for the next two quarters of next year. The highly automated plant produces graphics terminals for the computer products market. The company estimates that 700 terminals will need to be shipped to customers in the first quarter and 3200 in the second quarter. It takes an average of 5 hours of labour to produce each terminal and only 9 000 hours of straight labour are available. Overtime can be used, but the company has a policy of limiting the amount of overtime in each quarter to 10 percent of the straight time labour available. Labour costs R120 per hour at the straight-line rate and R180 per hour at the overtime rate. If a terminal is produced in one quarter and shipped in the next quarter, a carrying cost of R500 is incurred. The objective is to determine how many terminals should be produced on straight-line and overtime in each of first and second quarter to minimise straight-time labour, overtime labour and carrying costs.

a) Define your decision variables explicitly.

b) Formulate this aggregate planning problem as a linear program (LP).

c) Solve this model using SOLVER, or any suitable approach.

d) Write down the optimal solution and the associated total costs.

e) Analyse the resource utilisation as seen from the optimal solution.