Question

A company manufactures two types of chemicals Aand B. Each chemical requires two types of raw material P and Q. The table below shows number of units of P and Q required to manufacture one unit of A and one unit of B and the total availability of P and Q.

Chemical→	A	B	Availability
Raw Material ↓
P	3	2	120
Q	2	5	160

The company gets profits of ₹ 350 and ₹ 400 by selling one unit of A and one unit of B respectively. (Assume that the entire production of A and B can be sold). How many units of the chemicals A and B should be manufactured so that the company gets a maximum profit? Formulate the problem as LPP to maximize profit.

Answer 1

Let the company manufactures x units of chemical A and y units of chemical B. Then the total profit to the company is p = ₹(350x + 400y).

This is a linear function that is to be maximized. Hence, it is an objective function.

The constraints are as per the following table:

Chemical→	A (x)	B (y)	Availability
Raw Material ↓
P	3	2	120
Q	2	5	160

The raw material P required for x units of chemical A and y units of chemical B is 3x + 2y. Since the maximum availability of P is 120, we have the first constraint as 3x + 2y ≤ 120.

Similarly, considering the raw material Q, we have 2x + 5y ≤ 160.

Since, x and y cannot be negative, we have, x ≥ 0, y ≥ 0.
Hence, the given LPP can be formulated as:

Maximize p = 350x + 400y, subject to

3x + 2y ≤ 120, 2x + 5y ≤ 160, x ≥ 0, y ≥ 0