The Burnley Division of Turf Moor Industries manufactures different types of motors including motors used in ceiling fans. The Adamson Division of Turf Moor Industries manufactures ceiling fans, buying the motors from the Burnley Division or from an outside supplier. Both divisions are free to buy and sell outside the company and operate in a market of imperfect competition (as the divisions sell more, the selling price per unit declines). The Burnley Division has a variable cost of £10 per motor, and its total contribution margin at different sales levels and prices are estimated to be as follows:

The Adamson Division has a variable cost, other than the cost of the motor, of £30 per fan.
Selling prices for the ceiling fans at different sales levels are estimated to be as follows:

Total contribution margins from fans for the firm at different sales levels and prices are estimated to be as follows:

Total variable cost to the firm is the £10 variable cost to manufacture the motor plus the £30 variable cost of the Adamson Division.

Required

(a) Determine the number of motors the Burnley Division would want to produce and sell.

(b) If the Burnley Division insists on charging £40 per motor, determine the number of fans the Adamson Division would want to produce and sell.

(c) Determine the volume level that would maximise the firm’s profits.

(d) If the optimum volume level for the firm is used:
(i) determine the minimum transfer price that Burnley, the selling division, would accept; and (ii) determine the maximum transfer price Adamson, the buying division, would be willing to pay.

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Price () Variable cost Contribution Total per unit volume Contribution margin () () (units) () 40 34 422 10 30 10,000 300,000 10 24 12,000 288,000 28 10 18 14,000 252,000 22 10 12 16,000 192,000