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Math Help - dimensions of a animal pen

  1. #1
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    Exclamation dimensions of a animal pen

    I tried using the second derivative and setting it equal to zero. Then plugging that number into 60 = LW (A = LW) to find the other side. I then put those numbers into the perimeter formula P = 3w + L. For some reason I keeping getting it wrong. What should I be doing instead?

    A prize winning animal is going to be shown at the State Fair. A pen must be constructed to hold the animal. The rectangular pen will have three wooden sides, which cost 20 dollars per foot to construct. The front of the pen will be made of a special reinforced glass, which costs 50 dollars per foot to construct.
    The animal requires an area of 60 square feet in order to be comfortable.




    A) If the pen is to be built as cheaply as

    possible, what are the dimensions of the pen that should be built?

    L = ?

    W = ?



    B) How much will the pen cost to build?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Babs0201 View Post
    I tried using the second derivative and setting it equal to zero. Then plugging that number into 60 = LW (A = LW) to find the other side. I then put those numbers into the perimeter formula P = 3w + L. For some reason I keeping getting it wrong. What should I be doing instead?

    A prize winning animal is going to be shown at the State Fair. A pen must be constructed to hold the animal. The rectangular pen will have three wooden sides, which cost 20 dollars per foot to construct. The front of the pen will be made of a special reinforced glass, which costs 50 dollars per foot to construct.
    The animal requires an area of 60 square feet in order to be comfortable.




    A) If the pen is to be built as cheaply as

    possible, what are the dimensions of the pen that should be built?

    L = ?

    W = ?



    B) How much will the pen cost to build?
    $_________________
    xy=60

    and P=2x+2y

    you are trying to minimize y
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  3. #3
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    Quote Originally Posted by Babs0201 View Post
    I tried using the second derivative and setting it equal to zero. Then plugging that number into 60 = LW (A = LW) to find the other side. I then put those numbers into the perimeter formula P = 3w + L. For some reason I keeping getting it wrong. What should I be doing instead?

    A prize winning animal is going to be shown at the State Fair. A pen must be constructed to hold the animal. The rectangular pen will have three wooden sides, which cost 20 dollars per foot to construct. The front of the pen will be made of a special reinforced glass, which costs 50 dollars per foot to construct.
    The animal requires an area of 60 square feet in order to be comfortable.




    A) If the pen is to be built as cheaply as

    possible, what are the dimensions of the pen that should be built?

    L = ?

    W = ?



    B) How much will the pen cost to build?
    $_________________
    First of all, the perimeter is 2L + 2W, but that isn't actually what you are interested in. We have that the cost (C) of three sides is $20 per foot, and one is $50 per foot: C = 20L + 20W + 20L + 50W= 40L + 70W. Now, given that LW = 60, we want to minimize 40L + 70W. So we substitute L = \frac{60}{W} and then we have that cost C = \frac{2400}{W} + 70W. Now all you have to do is minimize C in terms of W.
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  4. #4
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    so I got $820, which was correct. Thank you!!!
    so
    w should = 6 ?
    L should =10 ?
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  5. #5
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    Quote Originally Posted by Babs0201 View Post
    so I got $820, which was correct. Thank you!!!
    so
    w should = 6 ?
    L should =10 ?
    I actually computed W = \sqrt\frac{240}{7}, which is slightly less than 6.
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