A manufacturer has a maximum of 240, 360, and 180 kilograms of wood, plastic and steel available. The company produces two products, A and B. Each unit of A requires 1, 3 and 2 kilograms of wood, plastic and steel respectively; each unit of B requires 3, 4 and 1 kilograms of wood, plastic and steel respectively. The profit per unit of A and B is $4.00 and $6.00 respectively.

a) Write out the objective profit function.

b) Write out the constraints this company faces.

c) Calculate (with details) and list all corner points and determine which combination of items will produce the maximum profit.