Question

A company manufactures two types of fertilizers F₁ and F₂. Each type of fertilizer requires two raw materials A and B. The number of units of A and B required to manufacture one unit of fertilizer F₁ and F₂ and availability of the raw materials A and B per day are given in the table below:

Fertilizers→	F1	F2	Availability
Raw Material ↓
A	2	3	40
B	1	4	70

By selling one unit of F₁ and one unit of F₂, the company gets a profit of ₹ 500 and ₹ 750 respectively. Formulate the problem as LPP to maximize the profit.

Answer 1

Let the company manufactures x units of fertilizers F₁ and y units of fertilizers F₂. Then the total profit to the company is z = ₹(500x + 750y).

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

Fertilizers→	F1	F2	Availability
Raw Material ↓
A	2	3	40
B	1	4	70

The raw material A required for x units of Fertilizers F₁ and y units of Fertilizers F₂ is 2x + 3y. Since the maximum availability of A is 40, we have the first constraint as 2x + 3y ≤ 40.

Similarly, considering the raw material B, we have x + 4y ≤ 70.

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

Maximize z = 500x + 750y, subject to

2x + 3y ≤ 40, x + 4y ≤ 70, x ≥ 0, y ≥ 0