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Math Help - Hello

  1. #16
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    Re: Hello

    Along border 2x + 3y = 240.
    (x,y) at corner points are (0,80) & (30,60).

    p=0.5x+0.4y
    At (0,80), p=32.
    At (30,60), p= (0.5*30)+(0.4*60)=15+24=39.

    Profit is maximized at $39 when sliderule sales are 30 units and sweatshirt sales are 60 units.

    {I've seen the importance of plotting graphs to understand this concept. Thank you Romsek!}
    Last edited by scwmba; December 15th 2013 at 03:34 AM.
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  2. #17
    MHF Contributor
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    Re: Hello

    Well done!

    I'll ask you to think about one more thing so this really sinks in.

    It's clear you make more money on slide rules than sweatshirts from the fact that 0.5 > 0.4.

    So intuitively you want to sell as many slide rules as possible. But what happens is that you end up wasting salesgirls time while the cashier catches up.

    Look at your graph. What does your intuition tell you about where the maximum profit should lie.

    As we increase the number of sweatshirts sold we modestly decrease the number of slide rules sold. Then at x=30 that number starts to rapidly decrease. That rapid decrease in sales of our most profitable item can't be good.

    So at what point do you think would be the maximum profit?
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  3. #18
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    Re: Hello

    Hello.

    I think that, when increasing number of sweatshirts, the maximum profit will be at point furthest away from origin, just before rapid decrease, which is (30,60).
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