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.

Let the merchant stock x desktop computers and y portable computers.
Let P be the profit.
Table

We are to maximise
P = 4500 x + 5000 y
subject to constraints
x + y ≤ 250
25000 x + 40000 y ≤ 7000000
or    5 x + 8 y ≤ 1400
x ≥ 0, y ≥ 0
Consider a set of rectangular cartesian axes OXY in the plane.
It is clear that any point which satisfies a ≥ 0, y ≥  0 lies in the first quadrant.
Now we draw the graph of x + y = 250
For x = 0, y = 250
For y = 0, x = 250
∴  line meets OX in A(250, 0) and OY in L(0, 250)
Again we draw the graph of 5 x + 8 y = 1400
For x = 0, 8 y = 1400 or y = 175
For y = 0, 5 x = 1400 or y = 280
∴ line meets OX in B(280, 0) and OY in M(0, 175).

Since feasible region satisfies all the constraints.
∴  OACM is the feasible region.
The comer points are O(0, 0), A(250, 0), C(200, 50), M(0, 175)
At O(0, 0), P = 4500 × 0 + 5000 × 0 = 0 + 0 = 0
At A(250, 0), P = 4500 × 250 + 5000 × 0 = 1125000
At C(200, 50), P = 4500 × 200 + 5000 × 50 = 900000 + 250000 = 1150000
At M(0, 175), P = 4500 × 0 + 5000 × 175 = 0 + 875000 = 875000
∴ maximum value = 1150000 at (200, 50)
∴ 200 units of desktop models and 50 units of portable models are to be stocked for maximum profit of Rs. 1150000.