# 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
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

Related Calculus and Beyond Homework Help News on Phys.org
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
Homework Helper
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

HallsofIvy