A farmer can grow two types of crop, A and B. The profit per unit of A is 3 and that for B is 2....

A farmer can grow two types of crop, A and B. The profit per unit of A is 3 and that for B is 2. Each unit of A requires one unit of labour, two units of land and three units of machine time, while for B the requirements are four of labour, one of land and one of machine time. There are 60 units of labour, 40 units of land and 50 units of machine time available.

(a) What should the farmer produce to maximise profits?

(b) Is it worthwhile renting 10 extra units of land at a total cost of 5?