Advanced: Calculation of optimal output level adopting a limiting factor approach and the computation of optimum selling prices using differential calculus AB p.l.c. makes two products, Alpha and Beta. The company made a £500000 profit last year and proposes an identical plan for the coming year. The relevant data for last year are summarized in Table 1.

Fixed costs were £480000 for the year, absorbed on machining hours which were fully utilized for the production achieved.
A new Managing Director has been appointed and he is somewhat sceptical about the plan being proposed. Furthermore, he thinks that additional machining capacity should be installed to remove any production bottlenecks and wonders whether a more flexible pricing policy should be adopted.
Table 2 summarizes the changes in costs involved for the extra capacity and gives price/ demand data, supplied by the Marketing Depart¬ ment, applicable to the conditions expected in the next period.
Table 2: Costs Extra machining capacity would increase fixed costs by 10% in total. Variable costs and machining times per unit would remain unchanged.LO1

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Table 1: Actuals for last year Product Product Alpha Beta Actual production and sales 20 000 40 000 (units) Total costs per unit 20 40 Selling prices per unit 25 50 (25% on cost) Machining time per unit 2 1 (hours) Potential demand at above 30000 50000 selling prices (units)