Calculus - optimization problem

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
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


Science Advisor
V= whl is one equation. Can you use the "lagrange multiplier" method?
i know how to use lagrange.. but i was told not to for this question
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


Science Advisor
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
im missing an equation then, which im having trouble finding....
I just dont understand how to find this other equation

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