Advanced: Limiting factor resource allocation and comparison of marginal revenue to determine optimum output and price

(a) A manufacturer has three products, A, B. and C. Currently sales, cost and selling price details and processing time requirements are as follows:

The firm is working at full capacity (13500 processing hours per year). Fixed manufacturing overheads are absorbed into unit costs by a charge of 200% of variable cost. This procedure fully absorbs the fixed manufacturing overhead.
Assuming that:
(i) processing time can be switched from one product line to another, (ii) the demand at current selling prices is:

and (iii) the selling prices are not to be altered, You are required to calculate the best production programme for the next operating period and to indicate the increase in net profit that this should yield. In addition identify the shadow price of a processing hour. (11 marks)

(b) A review of the selling prices is in progress and it has been estimated that. for each product, an increase in the selling price would result in a fall in demand at the rate of 2000 units for an increase of £1 and similarly, that a decrease of £1 would increase demand by 2000 units. Specifically the follow1ng price/demand relationships would apply:

From this information you are required to calculate the best selling prices. the revised best production plan and the net profit that this plan should produce.

Transcribed Image Text:

Product Product Product A B C Annual sales (units) 6000 6000 750 Selling price () 20.00 31.00 39.00 Unit cost () 18.00 24.00 30.00 Processing time required per unit (hours) 1 2