Advanced: Calculation of optimum price using calculus.

is reviewing the selling price of one of its products. The current selling price of the product is $25 per unit and annual demand is forecast to be 150000 units at this price. Market research indicates that the level of demand would be affected by any change in the selling price. Detailed analysis from this research shows that for every $1 increase in selling price, annual demand would reduce by 25000 units and that for every

$1 decrease in selling price, annual demand would increase by 25000 units.

A forecast of the annual costs that would be incurred by WX in respectof this product at differing activity levels is as follows:

The cost behaviour patterns represented in the above forecast will apply for the whole range of output up to 300000 units per annum of this product.

Required: z

(a) (i), Calculate the total variable cost per unit. (2 marks)
(ii) Calculate the selling price of the product that will maximize the company’s profits. (4 marks)
Note: If Price (P) = a — bx then Marginal Revenue = a — 2bx

(b) Explain TWO reasons why the company might decide NOT to use this optimum selling price. (4 marks)
CIMA P2 Performance Management

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Annual production (units) 100000 160000 200000 $000 $000 $000 Direct materials 200 320 400 Direct labour 600 960 1200 Overhead 880 1228 1460