Let the merchant stock x number of desktop models and y number of portable models.
∴ x and y ≥ 0
According to the given condition
The cost of a desKtop model is Rs25000 and that of a portable model is Rs 40,000. The merchant can invest up to Rs 7000000
⇒ 25000x + 40000y ≤ 7000000
⇒ 5x + 8y ≤ 1400
The monthly demand of computers will not exceed 250 units.
⇒ x+ y ≤ 250
The profit on a desktop model is Rs 4500 and the profit on a portable model is Rs5000.
Total profit , Z = 4500x + 5000y
Thus the mathematical formulation of the data is
Maximize Z = 4500x + 5000y
Subject to constraints
5x + 8y ≤ 1400
x+ y ≤ 250
x and y ≥ 0
the feasible region by the system of constraints is as follows:
The cornet points are A(250,0) , B( 200,50) and C(0 ,175)
The value of Z at the given corners points are:
The maximum value of Z is Rs1150000 at ( 200,50)
Thus the merchant should stock 200 desktop models and 50 portable models to earn the maximum profit of Rs 11, 50, 000.
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