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17. A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A requires 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is ?.5 each for type A and ?.6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize the profit?

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 company manufacture x souvenirs of type A and y souvenirs of type B. Therefore,

    x ≥ 0 and y ≥ 0

    The given information can be complied in a table as follows.

     

    Type A

    Type B

    Availability

    Cutting (min)

    5

    8

    3 × 60 + 20 =200

    Assembling (min)

    10

    8

    4 × 60 = 240

    The profit on type A souvenirs is Rs 5 and on type B souvenirs is Rs 6. Therefore, the constraints are

     5x + 8y ≤ 200

    10x + 8y ≤ 240 i.e.,5x + 4y ≤ 120

    Total profit, Z = 5x + 6y

    The mathematical formulation of the given problem is

    Maximize Z=5x +6y …(1)

    subject to the constraints,

     5x + 8y ≤ 200 … (2)

    5x + 4y ≤ 120 … (3)

    x, y ≥ 0 … (4)

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

    The corner points are A (24, 0), B (8, 20), and C (0, 25).

    The values of Z at these corner points are as follows

    The maximum value of Z is 200 at (8, 20).

    Thus, 8 souvenirs o

    ...more

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