Question

A wholesale merchant wants to start the business of cereal with Rs. 24000. Wheat is Rs. 400 per quintal and rice is Rs. 600 per quintal. He has capacity to store 200 quintal cereal. He earns the profit Rs. 25 per quintal on wheat and Rs. 40 per quintal on rice. If he stores x quintal rice and y quintal wheat, then for maximum profit the objective function is

• A. 25x + 40y
• B. 40x + 25y
• C. 400x + 600y
• D. $\frac{400}{40}x + \frac{600}{25}y$

Answer 1

Answer: (B)

40x + 25y

Answer 2

Let x be the quantity of rice in quintals and y be the quantity of wheat in quintals.

The profit on rice is Rs. 40 per quintal.

The profit on wheat is Rs. 25 per quintal.

The total profit is the sum of the profit from selling x quintals of rice and the profit from selling y quintals of wheat.

Profit from rice = (Profit per quintal of rice) × (Quantity of rice) = 40x.

Profit from wheat = (Profit per quintal of wheat) × (Quantity of wheat) = 25y.

The total profit, denoted by Z, is the sum of the profits from rice and wheat:

Z = 40x + 25y.

This function Z is the objective function that the merchant wants to maximize.