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Math Help - Optimization Problem.

  1. #1
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    Optimization Problem.

    Hey guys, I think I know the procedure, but something about my answer is wrong. Can someone post a solution for this?

    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 500 meters squared. If a brick wall costs $1200/m while a glass wall costs $600/m, what dimensions would minimize the cost of the showroom?
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  2. #2
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    Re: Optimization Problem.

    A better idea is for you to show us your own solution and we'll check where your mistake is...
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  3. #3
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    Re: Optimization Problem.

    Let x be the length of the showroom and y the width. We know that the area xy=500mē, so y=500/x.

    3 walls will be built with brick and just 1 will be of glass, so:

    C(x)=1200x+1200x+1200y+600y= 2400x+1800y= 2400x+1800(500/x)= 2400x+900000/x

    Now just find the derivative of C(x) and solve C'(x)=0.
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  4. #4
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    Re: Optimization Problem.

    What you have done is correct. Why do you think it's wrong?
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