Novacook Ltd makes two types of cooker, one electric and one gas. There are four stages in production of each of these, with the following features:
Manufacturing Stage Time need (hours) Total time available (hours per week)
Electric Gas
Forming 4 2 3,457
Machine shop 10 8 11,954
Assembly 6 4 5,437
Testing 2 2 2,106
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 program
b) Find the optimal solution to the problem