Calculus - optimization problem

  • Thread starter Pearce_09
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  • #1
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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
therefore
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
 

Answers and Replies

  • #2
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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
 
  • #3
HallsofIvy
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V= whl is one equation. Can you use the "lagrange multiplier" method?
 
  • #4
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i know how to use lagrange.. but i was told not to for this question
 
  • #5
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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
 
  • #6
HallsofIvy
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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
 
  • #7
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im missing an equation then, which im having trouble finding....
 
  • #8
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I just dont understand how to find this other equation
 

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