Question

A man has ₹1500 to purchase rice and wheat. A bag of rice and a bag of wheat cost ₹180 and 120 respectively. He has storage capacity of 10 bags only. He earns a profit of ₹11 and ₹8 per bag of rice and wheat respectively. How many bags of each must he buy to make maximum profit?

Answer 1

Let the number of wheat and rice bags be x and y. 

∴According to the question, 

120x + 180y ≤ 1500, x + y ≤ 10,x ≥ 0, y ≥ 0

Maximize Z = 8x + 11y 

The feasible region determined by 120x + 180y ≤ 1500, x + y ≤ 10,x ≥ 0, y ≥ 0 is given by

The corner points of feasible region are A(0,8), B(0,0), C(10,0), D(5,5) . 

The value of Z at corner point is

The maximum value of Z is 95 at point (5,5). 

Hence, the man should 5 bags each of wheat and rice to earn maximum profit.