Lulu hypermarket uses its own resources to make lighting equipment for sale in its superstores. It uses three types of factor input, namely labor, capital and raw material, in producing two products, X and Y. Each unit of X contributes AED 30 to profit, each unit of Y contributes AED 40 to profit.

To produce 1 unit of X requires 10 unit of labor, 10 unit of capital and 20 units of raw material.

To produce 1 unit of Y requires 10 unit of labor, 20 units of capital and 10 unit of raw material.

The firm has 50 units of labor, 80 units of capital and 80 units of raw material available.

Use a linear programming approach to find the feasible output combination of products X and Y that will maximize profit for Lulu.

What is the value of total profit at this combination?

In short

Maximize Z = 30X + 40Y

Subject to:

10X + 10Y 50 labor constraint

10X + 20Y 80 capital constraint

20X + 10Y 80 craw material constraint