Tough Optimization Question

Can someone send me the full steps so i can learn from it, i missed the lecture today so i didn't get the step by step walk through of the solution :( i'm having such a hard time with the optimization unit it's really tough... and our textbooks only give us to answer so i have no idea how to solve the question.

it's #6

http://smcewen.pbworks.com/f/Sec3_3+Extra+Practice.pdf

Re: Tough Optimization Question

Your restriction is the the volume must be 240

The volume in each box is given by $\displaystyle x^2y$ so $\displaystyle x^2y=240$

The area of wire that is needed is $\displaystyle 2(x)(2x)+2(x)(y)+(2x)(y)=4x^2+4xy$ the sum of the surface areas

Let $\displaystyle A=4x^2+4xy$

You want to minimise A so first get A in terms of only x, then find when $\displaystyle \frac{dA}{dx}$ equals zero, confirm that it is a minimum for the area not a maximum. You will probably get 2 answers, remember than you are restricted in how big/small x can be.