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