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18. 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 ? 70 lakhs and if his profit on the desktop model is ?. 4500 and on portable model is ?. 5000.

0 2 Views | Posted 4 months ago
Asked by Shiksha User

  • 1 Answer

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    Answered by

    Vishal Baghel | Contributor-Level 10

    4 months ago

    Let the merchant stock x desktop models and y portable models. Therefore,

    x ≥ 0 and y ≥ 0

    The cost of a desktop model is Rs 25000 and of a portable model is Rs 4000. However, the merchant can invest a maximum of Rs 70 lakhs.

    ∴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 Rs 5000.

    Total profit, Z=4500x +5000y

    Thus, the mathematical formulation of the given problem is

    Maximum Z=4500x+5000y             .....(1)

    subject to the constraints,

    5x +8y ≤ 1400        ....(2)

    ∴x + y ≤ 250       .....(3)

    x, y ≥ 01400        ......(4)

    The feasible region determined by the system of constraints is as follows.

    The corner points are A (250, 0), B (200, 50

    ...more

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