Formulate the plant’s strategy as a linear program to maximise the profit.

Question

A plant manufactures two products A and B, using three inputs, labour, material R and materials S. To make one unit of product A, it reqaures 6 kg of R and 7.5 kg of S, and 9 person-hours of labour. To make one unit of B it requires 12 kg of r and 4.5 kg of S nd 6 person-hours of labour. The demands for the products are such that the plant can sell as much of each of the product as it can produce. It earns a profit of Rs. 30 per unit of A and Rs.40 per unit of B. However only 900 kg of R and 675 kg of S and 1200 person-hours of labour are available each day.

1. Formulate the plant’s strategy as a linear program to maximise the profit.
2. Indicate the feasible region in a graphical representation of the problem.
3. Solve the problem graphically by finding the optimum operating point. What is the maximum profit?