Advanced: Allocation of scarce resources A processing company, EF, is extremely busy. It has increased its output and sales from 12 900 kg in quarter 1 to 17 300 kg in quarter 2 but, though demand is still rising, it cannot increase its output more than another 5% from its existing labour force which is now at its maximum.

Data in quarter 2 for its four products were:

The XY Company has offered to supply 2000 kg of product Q at a delivered price of 90% of EF’s selling price. The company will then be able to produce extra product P in its place up to the plant’s total capacity.
You are required to state, with supporting calcu¬ lations:

(a) whether EF should accept the XY Company’s offer; (10 marks)

(b) which would be the most profitable combina¬ tion of subcontracting 2000 kg of one product at a price of 90% of its selling price and producing extra quantities of another product up to the plant’s total capacity. Assume that the market can absorb the extra output and that XY’s quality and delivery are acceptable.

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Product Product Product Product P Q R S Output (kg) 4560 6960 3480 2300 Selling price ( per kg) 16.20 11.64 9.92 13.68 Costs ( per kg): Direct labour 1.96 1.30 0.99 1.70 (at 6 per hour) Direct materials 6.52 4.90 4.10 5.42 Direct packaging 0.84 0.74 0.56 0.70 Fixed overhead (absorbed on basis of direct labour cost) 3.92 2.60 1.98 3.40 Total 13.24 9.54 7.63 11.22