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Dimensions of box with largest volume

by evilpostingmong
Tags: dimensions, largest, volume
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evilpostingmong
#1
Aug27-08, 07:14 PM
P: 341
1. The problem statement, all variables and given/known data
Find the dimensions of a rectangular box with the largest volume with surface area 64cm^2.



2. Relevant equations
area of a rectangular prism 2xy+2yz+2xz


3. The attempt at a solution
took 2xy+2yz+2xz=64
rearranging for z:
z=(xy-32)/(y+x)
partial derivative of z with respect to x
y/(y+x)-(xy-32)/(y+x)^2
partial derivative of z with respect to y
x/(y+x) -(xy-32)/(y+x)^2
setting both derivatives equal to zero to obtain the critical point....
Here's where I hit a wall-
I cannot get a real root for y.
y/(y+x)-(xy-32)/(y+x)^2
y^2+xy=xy-32
y^2=-32
Please only help me up to this point until I ask you to help me further, I
want to challenge myself. Thank you!
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granpa
#2
Aug27-08, 07:27 PM
P: 2,258
what are you maximizing?
evilpostingmong
#3
Aug27-08, 07:32 PM
P: 341
The volume of this box.

granpa
#4
Aug27-08, 07:38 PM
P: 2,258
Dimensions of box with largest volume

you're maximizing xyz?
evilpostingmong
#5
Aug27-08, 07:45 PM
P: 341
Oh wait I'm finding the maximum dimensions that can be used to get the surface area of 64cm^2. So I maximize 2xy+2yz+2xz=64
granpa
#6
Aug27-08, 08:01 PM
P: 2,258
'maximum dimensions'?
evilpostingmong
#7
Aug27-08, 08:06 PM
P: 341
The problem states that I must find the dimensions of a rectangular box with the largest volume if it's total surface area is 64cm^2. What we don't know is how long those dimensions are.
granpa
#8
Aug27-08, 08:19 PM
P: 2,258
first you should find the maximum volume of a box with surface area 64cm^2.
evilpostingmong
#9
Aug27-08, 08:22 PM
P: 341
Okay! I'll take the problem from there and tell you how I made out.


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