Advanced: Optimal output, shadow prices and decision making using the graphical approach The instruments department ofMax Ltd makes two products: the XL and the YM. Standard revenues and costs per unit for these products are shown below:

Plating is a separate automated operation and the costs of £12 per hour are for plating materials and electricity.
In any week the maximum availability of inputs is limited to the following:

A management meeting recently considered ways of increasing the profit of the instrument depart¬ ment. It was decided that each of the following possible changes to the existing situation should be examined independently of each other.
(1) The selling price of product YM could be increased.
(2) Plating time could be sold as a separate service at £16 per hour.
(3) A new product, ZN, could be sold at £240 per unit. Each unit would require the following:

(4) Overtime could be introduced and would be paid at a premium of 50% above normal rates.
Requirements:

(a) Formulate a linear programme to determine the production policy which maximizes the profits of Max Ltd in the present situation (i.e. ignoring the alternative assumptions in 1 to 4 above), solve, and specify the optimal product mix and weekly profit. (6 marks)

(b) Determine the maximum selling price of YM at which the product mix calculated for requirement

(a) would still remain optimal.
(3 marks)

(c) Show how the linear programme might be modified to accommodate the sale of plating time at £16 per hour (i.e. formulate but do not solve). (3 marks)

(d) Using shadow prices (dual values), calculate whether product ZN would be a profitable addition to the product range. (4 marks)

(e) Ignoring the possibility of extending the product range, determine whether overtime working would be worthwhile, and if so state how many overtime hours should be worked. (3 marks)

(f) Discuss the limitations of the linear program¬ ming approach to the problems of Max Ltd.

Transcribed Image Text:

XL YM () () () () Selling price 200 180 Variable costs: Material A (10 per kg) (40) (40) Direct labour (32) (16) (8 per hour) Plating (12 per hour) (12) (24) Other variable costs (76) (70) (160) (150) Fixed overheads (allocated at 7 per direct labour hour) (28) (14) Standard profit per unit 12 16