Question - Conduct a linear programming procedure using either the graphical or the profit line approach to find the optimal solution i.e. maximum profit.

Scenario - A car manufacturer produces two versions of its popular medium sized model: a hatchback aimed at the family market and a coupe designed to appeal to affluent single customers. Both are based on the same chassis and differ only in the body kit used to make up the cars. They are both produced at the same factory.

There are 80,000 hours of manpower and 3,250 basic chassis units (one per vehicle) available each week. The hatchback takes five hours of assembly time while a coupe takes ten hours. At least 2,000 coupe models should be produced per week. Production is also constrained by the fact that owing to problems with a supplier only 25,000 locking mechanisms are available per week. A hatchback uses five of these locking mechanism while a coupe uses two.

The profit to the factory on a hatchback model is estimated to be 1,750 while the

profit on a coupe is 2,750. The market demand for the cars is high. It is known that demand will exceed production for time to come so they should be able to sell whatever mix of cars is produced. The car manufacturer wants to maximise its profits, but doesnt know what combination of versions of its medium-sized model to produce.