3.6 Darmor Ltd has three products, which require the same production facilities. Information about the production costs for one unit of its products is as follows:

Product 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.

Intermediate Products Ltd produces four types of water pump. Two of these (A and B) are sold by the business. The other two (C and D) are incorporated, as components, into another of the business’s products. Neither C nor D is incorporated into A or B. Costings (per unit) for the products are as follows:
A B C D £ £ £ £
Variable materials 15 20 16 17 Variable labour 25 10 10 15 Other variable costs 5 3 2 2 Fixed costs 20 8 8 12 £65 £41 £36 £46 Selling price (per unit) £70 £45 There is an outside supplier who is prepared to supply unlimited quantities of products C and D to the business, charging £40 per unit for product C and £55 per unit for product D.
Next year’s estimated demand for the products, from the market (in the case of A and B) and from other production requirements (in the case of C and D) is as follows:

Units A 5,000 B 6,000 C 4,000 D 3,000 For strategic reasons, the business wishes to supply a minimum of 50 per cent of the above demand for products A and B.
Manufacture of all four products requires the use of a special machine. The products require time on this machine as follows:
Hours per unit A 0.5 B 0.4 C 0.5 D 0.3 Next year there are expected to be a maximum of 6,000 special-machine hours available.
There will be no shortage of any other factor of production.
Required:

(a) State, with supporting workings and assumptions, which products the business should plan to make next year.

(b) Explain the maximum amount that it would be worth the business paying per hour to rent a second special machine.

(c) Suggest ways, other than renting an additional special machine, that could solve the problem of the shortage of special machine time.