Advanced: Optimal output with a single limiting factor and interpretation of a final matrix Hint: Reverse the signs in the final matrix.

(a) Corpach Ud manufactures three products for which the sales maxima, for the forthcoming year, are estimated to be:

Summarized unit cost data are as follows:

The allocation of fixed processing costs has been derived from last year's production levels and the figures may need revision if current output plans are different.
The established selling prices are:

The products are processed on machinery housed in three buildings:
Building A contains type A machines on which 9800 machine hours are estimated to be available in the forthcoming year. The fixed overheads lor this building are £9800 p.a.
Building B1 contains type B machines on which 10500 machine hours are estimated to be available in the forthcoming year.
Building B2 also contains type B machines and again 1 0 500 machine hours are estimated to be available in the forthcoming year.
The fixed overheads for the B1 and B2 buildings are, in total, £11200 p.a.
The times required lor one unit of output lor each product on each type of machine. are as follows:

Assuming that Corpach ltd wishes to maximize its profits for the ensuing year. you are required to determine the optimal production plan and the profit that this should produce.

{b) Assume that, before the plan that you have prepared in part

(a) is implemented, Corpach ltd suffers a major fire which completely destroys building B2. The fire thus reduces the availability of type B machine time to 1 0 500 hours p.a. and the estimated fixed overhead for such machines, to £8200.
In all other respects the conditions set out, in part {a) to this question. continue to apply In his efforts to obtain a revised production plan the company's accountant makes use of a linear programming computer package. This package produces the following optimal tableau:

In the above: lis the total contribution, X1 is the budgeted output of product 1, X2 is the budgeted output of product 2, X3 is the budgeted output of product 3, S1 is the unsatisfied demand for product 1 , S2 is the unsatisfied demand for product 2, S3 is the unsatisfied demand for product 3, S4 is the unutilized type A machine time S5 is the unutilized type B machine time.
and The tableau is interpreted as follows:
Optimal plan - Make 2500 units of Product 1, 1850 units of Product 2, 1200 units of Product 3, Shadow prices- Product1 £1 .50 per unit, Type A Machine Time £2.429 per hour Type B Machine Time £0.714 per hour.
Explain the meaning of the shadow prices and cons1der how the accountant might make use of them. Calculate the profit anticipated from the revised plan and comment on its variation from the profit that you calculated in your answer to part (a). (9 marks)

(c) Explain why linear programming was not necessary for the facts as set out in part

(a) whereas it was required for part (b)

Transcribed Image Text:

Product 1 Product 2 57500 Product 3 96000 125 000