# Calculus - optimization problem

#### Pearce_09

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

#### FunkyDwarf

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

#### HallsofIvy

V= whl is one equation. Can you use the "lagrange multiplier" method?

#### Pearce_09

i know how to use lagrange.. but i was told not to for this question

#### Pearce_09

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

#### HallsofIvy

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

#### Pearce_09

im missing an equation then, which im having trouble finding....

#### Pearce_09

I just dont understand how to find this other equation

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