Question -
Answer -
Let the merchant stock x desktop models and y portable modelsrespectively.
Hence,
x ≥ 0 and y ≥ 0
Given that the cost of desktop model is Rs 25000 and of aportable model is Rs 40000.
However, the merchant can invest a maximum of Rs 70 lakhs
Hence, 25000x + 40000y ≤ 7000000
5x + 8y ≤ 1400
The monthly demand of computers will not exceed 250 units.
Hence, x + y ≤ 250
The profit on a desktop model is 4500 and the profit on aportable model is Rs 5000
Total profit, Z = 4500x + 5000y
Therefore, the mathematical formulation of the given problem is
Maximum Z = 4500x + 5000y ………… (i)
Subject to the constraints,
5x + 8y ≤ 1400 ………… (ii)
x + y ≤ 250 ………….. (iii)
x, y ≥ 0 …………. (iv)
The feasible region determined by the system of constraints isgiven below
A (250, 0), B (200, 50) and C (0, 175) are the corner points.
The values of Z at these corner points are given below
| Corner point | Z = 4500x + 5000y | |
| A (250, 0) | 1125000 | |
| B (200, 50) | 1150000 | Maximum |
| C (0, 175) | 875000 | |
The maximum value of Z is 1150000 at (200, 50)
Therefore, the merchant should stock 200 desktop models and 50portable models to get the maximum profit of Rs 1150000.