Question

use Lagrange Multipliers to solve.
A rectangular tank with a bottom and sides but no top is to have volume 500 cubic feet. Determine the dimensions (length, width, height) with the smallest possible surface area.

Answer 1

you need amistre for this. he is a lagrange multiplier user

Answer 2

bookmarking for future reference.

Answer 3

l*b*h=500
l*b+2(b*h+l*h)=surface area
diiferentate the first eq to get b*h dl +l*b dh + l*h db=0
differentiate the second to get