Question

Please Help!!
What is the maximum possible volume for a rectangular box (with square base and no top) made from 12 square feet of cardboard?

Answer 1

You know that area is \(12=4xy+x^2,\) and that volume is \(V=x^2y.\)
Using the first equation, write an expression for either (1) x in terms of y, or (2) y in terms of x. Then, substitute that expression into the volume equation appropriately, and find the critical points of V(x) or V(y), depending on the sub you make.