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Math Help - Help for derivative problem

  1. #1
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    Exclamation Help for derivative problem

    Hi friends

    Help for derivative problem


    a manufacturer of aquarium wants to make a large rectangular box-shaped aquarium that hold 64 ft^3 of water. if material for the base cost 20 per sq foot and for sides costs 10 dollar per sq foot, find the dimenions for which the cost of marerials will the least.


    please please help me
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  2. #2
    MHF Contributor matheagle's Avatar
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    Does this have a top?

    I would use LaGrange with xyz=64 as our constraint
    using x and y as the base and length and z as the height we have as our cost

    C=20xy +10(2xz)+10(2yz) IF you don't have a top

    otherwise it's C=20(2xy) +10(2xz)+10(2yz) if there is a top as well.
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  3. #3
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    Quote Originally Posted by matheagle View Post
    Does this have a top?

    I would use LaGrange with xyz=64 as our constraint
    using x and y as the base and length and z as the height we have as our cost

    C=20xy +10(2xz)+10(2yz) IF you don't have a top

    otherwise it's C=20(2xy) +10(2xz)+10(2yz) if there is a top as well.

    but what about

    the cost of materials will the least.
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