# A man has Rs 1500 to purchase rice and wheat

A man has Rs 1500 to purchase rice and wheat. A bag of rice and a bag of wheat cost Rs 180 and Rs 120 respectively. He has a storage capacity of 10 bags only. He earns a profit of Rs 11 and Rs 8 per bag of rice and wheat respectively. How many bags of each must he buy to make maximum profit? The answer given in the book is 5 bags of each.

Let the bags of rice purchased be x and bags of wheat purchased be y
Then, 180x + 120y<= 1500
Also, x+y <=10
And x>=0 and y>=0
Profit = 11x + 8y
Now, if you will draw the graph using the 4 constraint equations mentioned above,the common region would be a closed surface with A(0,0), B(8.33,0), C(5,5), D(0,10)
Hence, the profit would be maximum at one of the vertices only
Profit at A(0,0) = 11(0) + 8(0) = 0
Profit at B(8.33,0) = 11(8.33) + 8(0) = 91.63
Profit at C(5,5) = 11(5) + 8(5) = 95
Profit at D(0,10) = 11(0) + 8(10) =80
Hence, the maximum profit is at point C and hence, the man should purchase 5 bags of each rice and wheat to maximise his profit.