Question

A merchant plans to sell two types of personal computers — a desktop model and a portable model that will cost Rs. 25,000 and Rs. 40,000 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 his profit on the desktop model is Rs. 4,500 and on the portable model is Rs. 5,000. Make an L.P.P. and solve it graphically.

Answer 1

Let the number of desktop and portable computers to be sold be x and y respectively.

Here, Profit is the objective function Z. 

∴ Z = 4500x + 5000y …(i) 

we have to maximise z subject to the constraints 

x + y ≤ 250 …(ii) (Demand Constraint)

25000x + 40000y ≤ 70,00,000 …(iii) (Investment constraint) 

⇒ 5x + 8y ≤ 1400 

x ≥ 0, y ≥ 0 …(iv) (Non-negative constraint) 

On plotting graph of above constraints or inequalities, we get shaded region having corner point A, B, C as feasible region.

For coordinates of C, equation x + y = 250 and 5x + 8y = 1400 are solved and we get x = 200, y = 50 

Now, we evaluate objective function Z at each corner

Corner Points	Z = 4500x + 5000y
O(0, 0)	0
A(250, 0)	1125000
C(200, 50)	1150000 Maximum
B(0, 175)	875000

Maximum profit is Rs. 11,50,000 when he plan to sell 200 unit desktop and 50 portable computers.