A company makes and sells two products, clarinets and saxophones. The cost and revenue per unit information is predicted to be as follows:

Unit costs and revenues Clarinet Saxophone

Selling price 300 345

Variable costs Material 70 60

Variable overhead 10 15

Instrument case 40 40

Allocated fixed costs Direct labour 60 90

Overhead: machine related 40 30

other 20 30

Total cost 240 265

Profit 60 80

Labour is a fixed cost as the skilled personnel are paid by salary. They cannot easily be replaced. The allocation is based on a rate of 15 per hour and an assumption that 10,800 hours will be worked each year. Machine related costs refer to a specialist machine which is required for both types of musical instrument. The availability of this machine is 1800 hours per year and the fixed costs are 72,000. Other overhead is allocated based on skilled labour hours.

Required: (a) Past experience indicates that instruments are sold in the ratio 3 clarinets to 2 saxophones; calculate the number of each instrument which should be sold to break even for the year and the maximum profit which could be made with the current ratio of sales, given the skilled labour and specialist machine constraints. (b) The company would like to use the labour time and machine time to their maximum and would be prepared to incur additional advertising of 12,000 to change the sales mix if necessary. Calculate the optimal annual sales mix for the company and the profit improvement, assuming the company incurred the proposed advertising expenditure. (c) Explain the meaning of the term shadow price and explain how a shadow price can be used in decision making.