# Maximum and minimum applications

• Jun 24th 2012, 11:34 PM
brent94
Maximum and minimum applications
Hey guys, need a hand with a problem.

A cuboid parcel is to be tied with a length of string both across and longways, forming a cross on top of it. The parcel as a length of x, width of x and height of y. The fixed volume is 8000cm cubed.

Find the length, L, of string in terms of x and y.

What is the volume of the box in terms of x and y, and hence find y in terms of x.

Using the previous equation, find the length of string, L, in terms of x only.

What is the minimum length of L?

Thanks.
• Jun 25th 2012, 12:55 AM
biffboy
Re: Maximum and minimum applications
I get L=4x+4y V=x^2y So x^2y=8000 y=8000/x^2 S0 L=4x+32000/x^2 Then differentiate and put =0
• Jun 25th 2012, 01:15 AM
brent94
Re: Maximum and minimum applications
Ok so i did that, it came out x=25.2. That would be a side length yeah? So then i sub that into the L=4x+32000/x^2 equation to get L, then back into the L=4x+4y equation to get y?
• Jun 25th 2012, 04:00 AM
biffboy
Re: Maximum and minimum applications
Yes 25.2 is correct. You weren't asked to find L and x and y.