What would the answers be for questions (d), (e) and (f) without doing a re-run
ID: 3143437 • Letter: W
Question
What would the answers be for questions (d), (e) and (f) without doing a re-run of solver?
Please note: This question was solved with Excel Solver and not Lindo.
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 Solve this model using SOLVER or LINDO Write down the optimal solution and the associated total costs. (b) (c) 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. Give the optimal solution and total costs if amount of straight labour time available in quarter 2 is (i) 8750 hours, (ii) 8500 hours, (d) (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 quarterExplanation / Answer
Part d.
From the Sensitivity analysis, allowable increase and decrease in the straight-time hours in quarter 2 is 600 and 300. The shadow price which is valid for the given range of (9000 + 600 = 9600) and (9000 – 300 = 8700) is -160, beyond which the solution is infeasible. Thus if the available hours in quarter 2 is increased the cost is reduced by $160 per hour increase. If the hours are reduced then the cost will increase by R160 per decrease in hours.
Thus if the straight-time hours in quarter 2 is decreased to 8750, which is with the allowable limit, the cost will increase by (9000 – 8750 =) 250 x 160 = 40,000.
Thus total production cost is increased to 3,040,000 + 40,000 = R 3,080,000
If the available Straight-time hours in quarter 2 are reduced to 8,500 which beyond the allowable decrease limit, the solution will be infeasible, one of the constraint will not be satisfied.
Part E
The cost per straight-time hour is increased from R120 to R130, thus the straight-time labor cost per unit in quarter 1 will be 130*5 = R 650.
From sensitivity analysis, the allowable increase in the straight-time labor cost per unit in quarter 1 is 300 , thus the cost per unit can be increased to R600 + R300 = R900, so that the solution will remain optimal.
As the increase in cost per unit = 650 – 600 = 50, the solution remains same.
Thus, total cost = 3,040,000 + (50)(580) = 3,040,000 + 29,000 = R 3,069,000
The total cost will increase to R 3,069,000 if the straight-time cost per labor hour in quarter 1 is increased from R 120 to R 130.
part f
The sensitivity report gives allowable increase and decrease in the RHS of the constraint. The condition or the allowable increased or decreased limits in the constraints other than straight-time labor hours in quarter 2, it is possible to use all the available straight-time labor for quarter 2.
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