Novacook Ltd makes two types of cooker, one electric and one gas. There are four stages in the production of each of these, with the following features:

Each electric cooker has a variable cost of £200 and a selling price of £300, and each gas cooker has a variable cost of £160 and a selling price of £240. Fixed overheads are £60,000 a week and the company works a 50-week year. The marketing department suggests maximum sales of 800 electric and 1,250 gas cookers a week.
(a) Formulate this as a linear programme.
(b) Find the optimal solution to the problem, and draw a graph to illustrate its features.
(c) A company offers testing services to Novacook. What price should they be prepared to pay for this service, and how much should they buy?
(d) A new cooker is planned that would use the manufacturing stages for 4, 6, 6 and 2 hours respectively. At what selling price should Novacook consider making this cooker if the other variable costs are £168 aunit?

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Manufacturing stage Time needed (hours per unit) Total time available (hours a week) Electric Gas 3,600 12,000 Forming Machine shop 10 Assembly Testing 4 8 4 6,000 2,800 2