# Constrained Maximization

1. Mar 14, 2009

### MathNoob123

1. The problem statement, all variables and given/known data
A particular parcel sercive will accept only packages with length no more than 128 inches and length plus girth(xz)(width times height) no more than 145 inches.

What are the dimensions of the largest volume package the parcel service will accept?

This is the problem, but I just need to figure/know the objective equation and subject equation.
Do i use 2zx+2xy+2yz as my objective function and for my subject function would it be something like zx-17=0?

NOTICE: THIS IS A RECTANGULAR BOX

2. Relevant equations

Using Lagrange Multipliers
A=xy+xz+yz

3. The attempt at a solution

considering that i know that the area function is 2zx+2xy+2yz
Do i use 2zx+2xy+2yz as my objective function and for my subject function would it be something like zx-17=0?

2. Mar 14, 2009

### lanedance

hi mathnoob123

I'm not sure where you got that equation from

what is the volume of a package? this is what you're trying to maximise...

then the constraints are as given, you can have more than one

what is girth? are you sure is just not width as it is given in inches not a areal unit...
also you may have to be careful about x>y>z in defining length, width etc.

3. Mar 14, 2009

### MathNoob123

I have successfully solved this problem. Thank you to all my fans. I am slowly, but surely becoming a powerful mathmatician. Muuuuuuhahahahaahhahahha!!!!

4. Mar 15, 2009

### Staff: Mentor

The words and the expressions don't match here. The girth is how far around the package is. If the longest dimension of the package is z, then the girth would be 2x + 2y.
No and no. What you show for your objective function--2zx+2xy+2yz-- is just the area of the 6 sides of the package. And I have no idea where zx - 17 = 0 comes from.
What you want to do is maximize the volume of the package (xyz) subject to the length restraint and the girth restraint.

I'm glad you were able to solve this problem successfully. However, the work shown here would not lead to a successful conclusion, as far as I can see.