# Linear programming

“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 95,000 hours of manpower and 8,900 basic chassis units (one per vehicle) available each week. The hatchback takes 4 hours of assembly time while a coupe takes 6.5 hours.

At least 1,000 coupe models should be produced per week.

Production is also constrained by the fact that owing to problems with a supplier only 34,000 door handles are available per week. A hatchback uses 10 of these handles while a coupe uses 4.

The profit to the factory on a hatchback model is estimated to be £3,450 while the profit on a coupe is £975.

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 doesn’t know what combination of versions of its medium-sized model to produce.” Question 1: Graph the constraints and find the Solution space. Question 2: The car manufacturer wants to maximise its profits, what combination of versions of its medium-sized model to produce? Show your calculation and explanation.