A factory uses raw materials x and y to produce products A a

A factory uses raw materials x and y to produce products A and B. Each unit of product A requires 5 units of x and 3 of y; each unit of B, 3 of x and 6 of y. On hand there are 15 units of x and 18 units of y. The profits on the sales of A and B are 2 per unit and 3 per unit, respectively. How should the raw materials be used to realize a maximum profit?

Solution

Ans:

Given raw materials are 15 units of x and 18 units of y.

Let the profit maximising be such that there are m units of A and n units of B produced.

This would require 5m units of x and 3m units of y and 3n units of x and 6n units of y.

Solving for m and n we get m=1.7 and n=2.1

Thus, A would need 8.5 units of x and 5.1 units of y and B would need 6.4 units of x and 12.8 units of y .