# Tough Optimization Question

• Mar 12th 2013, 05:01 PM
Cindz83
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
• Mar 12th 2013, 07:19 PM
Shakarri
Re: Tough Optimization Question
Your restriction is the the volume must be 240
The volume in each box is given by $x^2y$ so $x^2y=240$

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

You want to minimise A so first get A in terms of only x, then find when $\frac{dA}{dx}$ 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.