Q: 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) Formulate this aggregate planning problem as a linear program. Define your decision variables explicitly.
(b) Solve this model using SOLVER or LINDO.
(c) Write down the optimal solution and the associated total costs. Use only the initial printout of the optimal solution to answer the following questions. (This means that you may not change the relevant parameters in the model and do re-runs.) Explain how you arrive at your answers.
(d) Give the optimal solution and total costs if amount of straight labour time available in quarter 2 is
(i) 8750 hours:
(ii) 8500 hours:
(e) What would the total costs be if amount of straight labour costs in quarter 1 is R130
(f) Under what circumstances will it be possible to use all the available straight- labour time for the second quarter.