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Calculus - optimization problem

  1. Sep 19, 2006 #1
    ok, i have an aquarium of volume V... where the cost of the base is 5 times of the sides... let h- height , w- width, l - lenght...
    therefore 2hw + 2hl is the cost of the sides and 5wl is the cost of the base
    total cost = 2hw + 2hl + 5wl --> min
    and i want find the dimensions to minimize cost.
    I know how to do problems like these ive done many, its just this one is somehow bothering me...
    i need to solve for 1 variable then i have a formula with 2 variables.. then i take the partial derivatives to see if my dimensions that i find indeed minimize cost. but for some reason i cant even get past my total cost formula.... help please
  2. jcsd
  3. Sep 19, 2006 #2
    You know the volume formula, so that in conjunction with your cost forumula will provide you with one variable in terms of another and bingo
  4. Sep 20, 2006 #3


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    V= whl is one equation. Can you use the "lagrange multiplier" method?
  5. Sep 20, 2006 #4
    i know how to use lagrange.. but i was told not to for this question
  6. Sep 20, 2006 #5
    I use my cost equation to solve for h and got
    h = -5wl / 2w + 2l
    and when i sub that into volume and partial derive but it doesnt make any sense.. I get l = w and then that implies that h = -10/8 ... not possible to have a negative number
  7. Sep 20, 2006 #6


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    No, you don't have a cost equation. You only have a cost function that you want to minimize. You don't know what it is equal to. (It certainly isn't equal to 0!) The only equation you have is V= whl
  8. Sep 20, 2006 #7
    im missing an equation then, which im having trouble finding....
  9. Sep 20, 2006 #8
    I just dont understand how to find this other equation
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