Q. 55.0( 2 Votes )

A merchant plans

Answer :

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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