Response to the following problem:
Darmor Ltd has three products, X, Y and Z, which require the same production facilities. Information about the production costs for one unit of its products is as follows
X Y Z
£ £ £
Labour: Skilled 6 9 3
Unskilled 2 4 10
Materials 12 25 14
Other variable costs 3 7 7
Fixed costs 5 10 10
All labour and materials are variable costs. Skilled labour is paid £12 an hour, and unskilled labour is paid £8 an hour. All references to labour costs, above, are based on basic rates of pay. Skilled labour is scarce, which means that the business could sell more than the maximum that it is able to make of any of the three products. Product X is sold in a regulated market, and the regulators have set a price of £30 per unit for it.
Required:
(a) State, with supporting workings, the price that must be charged for products Y and Z such that the business would find it equally profitable to make and sell any of the three products.
(b) State, with supporting workings, the maximum rate of overtime premium that the business would logically be prepared to pay its skilled workers to work beyond the basic time