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Math Help - Grr (optimization word problem)

  1. #1
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    Grr (optimization word problem)

    "A rectangular swimming pool is to be built with an area of 1800 sq. feet. The owner wants 5-foot wide decks along either side, and 10-foot wide decks at both ends. Find the dimensions of the smallest piece of property on which the pool can be built satisfying these conditions."

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  2. #2
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    Quote Originally Posted by Nitz456 View Post
    "A rectangular swimming pool is to be built with an area of 1800 sq. feet. The owner wants 5-foot wide decks along either side, and 10-foot wide decks at both ends. Find the dimensions of the smallest piece of property on which the pool can be built satisfying these conditions."
    Hello,

    1. I've attached a sketch of the described swimming pool.

    2. A_{water}=l\ \cdot \ w=1800. Thus: l=\frac{1800}{w}

    3. The area including the decks is:

    A=(l+20)\ \cdot \ (w+10). Now plug in the value of l:

    4. A(w)=(\frac{1800}{w}+20)\ \cdot \ (w+10). Expand the RHS of this equation:

    A(w)=1800+\frac{18000}{w}+20w+200=2000+\frac{18000  }{w}+20w

    5. This function has an extreme value (maximum or minimum, you are interested in the minimum) if the first derivative equals zero:

    A'(w)=-\frac{18000}{w^2}+20
    0=-\frac{18000}{w^2}+20. Solve for w:

    I've got: w = 30. Plug in this value to calculate l. I've got l = 60.

    EB
    Last edited by earboth; November 22nd 2006 at 05:07 AM. Reason: 1 line was missing
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  3. #3
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    Quote Originally Posted by Nitz456 View Post
    "A rectangular swimming pool ...
    Hello,

    it's me again. I forgot to attach the sketch. Here it is:

    EB
    Attached Thumbnails Attached Thumbnails Grr (optimization word problem)-schwimmbad_rand.gif  
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