Advanced: Calculation of optimum selling prices using differential calculus Alvis Taylor has budgeted that output and sales of his single product, flonal , will be 100000 units in 1982 At this level of activity his unit variable costs are budgeted to be £50 and his unit fixed costs £25. His sales manager estimates that the demand for flonal would increase by 1000 units for every decrease of £1 in unit selling price (and vice-versa), and that at a unit selling price of £200 demand would be nil.

Information about two price 1ncreases has just been received from suppliers. One is for materials (which are included in Alvis Taylor's variable costs), and one is for fuel (which is included in his fixed costs). Their effect will be to increase both the variable costs and the fixed costs by 20% in total over the budgeted figures.

Alvis Taylor aims to maximize profits from his business.

You are required, in respect of Alvis Taylor's business:

(a) to calculate, before the cost increases:

(i) the budgeted contribution and profit at the budgeted level of sales of 1 00 000 units, and

(ii) the level of sales at which profits would be maximized.

and the amount of those maximum profits, (7 marks)

(b) to show whether and by how much Alvis Taylor should adjust his selling price, in respect of the increases in, respectively:

(i) fuel costs

(ii) materials costs, (6 marks)

(c) to show whether and by how much it is worthwhile for Alvis Taylor, following the increases in costs, to spend £1 000000 on a TV advertising campaign if this were confidently expected to have the effect during 1982 (but not beyond then) that demand would still fall by 1000 units for every increase of £1 in unit selling price (and vice-versa). but that it would not fall to nil until the unit selling price was £210,

(5 marks)

(d) to comment on the results which you have obtained in

(a)-(

c) above and on the assumptions underlying them.