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Math Help - Linear Programming

  1. #1
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    Linear Programming

    An outdoor clothing manufacturer has 520 metres of polarfleece material. the manufacturer will use it to make jackets of two types, Polarbear and Polarfox, to sell to retailers. For each jacket of either type, 2.0 metres of material is required. However, the Polarbear is simpler in design, requiring 2.4 hours each in the production process while each Polarfox requires 3.2 hours. There are 672 hours available.
    From past experience of demand, the manufacturer has decided to make no more than half as many Polarfox jackets as Polarbear jackets. If the profit on each Polarbear jacket is $36 and the profit on each Polarfox jacket is $42, use a graphical method to find how many of each type should be made in order to maximise profit. What is the maximum profit?

    Well first of all, i tried to work out the constraints....
    x>- 2, y>- 2
    2.4x+3.2y-< 672
    y-< 1/2x
    P=36x+42y

    All of the three graphs do not intersect at the same point and therefore i'm not able to find x and y..........
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by benjiman View Post
    An outdoor clothing manufacturer has 520 metres of polarfleece material. the manufacturer will use it to make jackets of two types, Polarbear and Polarfox, to sell to retailers. For each jacket of either type, 2.0 metres of material is required. However, the Polarbear is simpler in design, requiring 2.4 hours each in the production process while each Polarfox requires 3.2 hours. There are 672 hours available.
    From past experience of demand, the manufacturer has decided to make no more than half as many Polarfox jackets as Polarbear jackets. If the profit on each Polarbear jacket is $36 and the profit on each Polarfox jacket is $42, use a graphical method to find how many of each type should be made in order to maximise profit. What is the maximum profit?

    Well first of all, i tried to work out the constraints....
    x>- 2, y>- 2
    2.4x+3.2y-< 672
    y-< 1/2x
    P=36x+42y

    All of the three graphs do not intersect at the same point and therefore i'm not able to find x and y..........
    Let b be the number of Polarbear jackets manufactured, and f be the number
    of Polarfox jackets manufactured.

    Time constraint:

    2.4b+3.2f <= 672

    Material constraint:

    2b+2f<= 520

    Experience constaint:

    f-2b<=0

    Implicit constaints:

    f>=0, b>=0.

    Objective:

    O=36b+42f

    RonL
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  3. #3
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    The intersection points of these are (168,84)
    which gives P=168*36+84*42=9576.

    The actual answer is (200, 60)
    Where the maximum profit is $9720.

    Can you fix it and work back there again...
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by benjiman View Post
    The intersection points of these are (168,84)
    which gives P=168*36+84*42=9576.

    The actual answer is (200, 60)
    Where the maximum profit is $9720.

    Can you fix it and work back there again...
    Have you checked all the vertices of the feasible region?

    Then check the other vertices.

    RonL
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