# Lagrange Multipliers for Volume

## Homework Statement

The Park Service is building shelters for hikers along the Appalachian Trail. Each shelter has a back, a top, and two sides. Find the dimensions that will maximize the volume while using 384 square feet of wood.

They want me to find the length, width, and height.

## Homework Equations

Here's my problem, I can't form a constraint for the problem because I don't know what they are looking for. The constraints I formed (two of them) did not work (they are below along with the formula I used).

F(x)=2zy+xz+xy
constraint used= Lambda(384-xyz)

and

f(x)=xyz
constraint used= lambda(384-2yz-xz-zy)

## The Attempt at a Solution

The answers I got are WAY off the correct answers. The correct answers are 16 (length) and 8 (for both width and height).

Can someone please tell me if I used the wrong equations, and if I did, how to form an equation from the given problem. I know how to calculate the answers, just not how to form the equation from a word problem. Thank you.

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