Question

A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.

Answer 1

P = 4500 x + 5000 y subject to 

(i) x + y ≤ 250 

(ii) 25000 x + 40000 y ≤ 7000000 

5x + 8y ≤ 1400 

x ≥ 0; y ≥ 0

ABCD is the solution region

A (0,0), P = 4500 x + 5000 y = 0 

B (250,0), P = 4500 x 250 = Rs 1125000 

C (200,50), P = 4500 x 200 + 5000 x 50 = Rs 1150000 

D (0,175), P = 5000 x 175 = Rs 875000 

∴ The profit is maximised at C (200,50) Rs 1150000