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Math Help - Optimization Problem

  1. #1
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    Optimization Problem

    Hi, I'm having problems with the following question. It's probably super easy... but I just keep getting the wrong answer.

    A showroom for a car dealership is to be built in the shape of a rectangle with brick on the back and sides, and glass on the front. The floor of the showroom is to have an area of 500m^2.
    a) If a brick wall costs $1200/m while a glass wall costs $600/m, what dimensions would minimize the cost of the showroom?

    When I try to solve for one of the variables I get, 2400L+1800W=500 Is this the right way to start it?

    Any help would be appreciated
    Last edited by sam314159265; June 4th 2010 at 12:12 PM.
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  2. #2
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    Quote Originally Posted by sam314159265 View Post
    Hi, I'm having problems with the following question. It's probably super easy... but I just keep getting the wrong answer.

    A showroom for a car dealership is to be built in the shape of a rectangle with brick on the back and sides, and glass on the front. The floor of the showroom is to have an area of 500m^2.
    a) If a brick wall costs $1200/m while a glass wall costs $600/m, what dimensions would minimize the cost of the showroom?

    When I try to solve for one of the variables I get, 2400L+1800W=500 Is this the right way to start it?

    Any help would be appreciated
    What you want is to minimize S = 1200(2L+W) +  600W subject to LW = 500 .
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  3. #3
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    So should I set the equation equal to zero? I tried that and got W=-3L/4, but when I plug that into A=LW and take the derivative to solve for W, I got W=8/3.... I'm not entirely sure what I'm doing wrong
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  4. #4
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    Quote Originally Posted by sam314159265 View Post
    So should I set the equation equal to zero? I tried that and got W=-3L/4, but when I plug that into A=LW and take the derivative to solve for W, I got W=8/3.... I'm not entirely sure what I'm doing wrong
    Using  LW = 500, eliminate either L or W in S. This then gives a function of one variable. Now use calculus.
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  5. #5
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    This is probably going to sound dumb, but what is "S"? Thanks for helping me btw
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