What is the optimal volume of a box with given dimensions using calculus?

[Elihu5991]

Homework Statement

SEE QUESTION IMAGE

Homework Equations

SEE ABOVE

The Attempt at a Solution

SEE WORKINGS IMAGE

 

[ehild]

Can you type in your work?

ehild

 

[Elihu5991]

Sorry that my handwritiing is too messy and scan isn't done right. Just trying to get this done ASAP.

(25-2x)(40-2x)

y=(25-2x)(-2)+(40-2x)(-2)
=-50+4x-40+2x
=-90+6x
x=15

Not sure what to next do.

 

[Ray Vickson]

Sorry that my handwritiing is too messy and scan isn't done right. Just trying to get this done ASAP.

(25-2x)(40-2x)

y=(25-2x)(-2)+(40-2x)(-2)
=-50+4x-40+2x
=-90+6x
x=15

Not sure what to next do.

Is x the length of the corner pieces cut out? If so, you need to define it in words; a formulation without an explanation is worth 0.

Also, is (25-2x)*(40-2x) the thing you want to maximize? Why? What does the box look like if you use your proposed solution of x = 15?

 

[eumyang]

Sorry that my handwritiing is too messy and scan isn't done right. Just trying to get this done ASAP.

(25-2x)(40-2x)

y=(25-2x)(-2)+(40-2x)(-2)

You mean y', not y.

Also, I'm guessing that you want to maximize the volume. If so, then
y = (25-2x)(40-2x)
as the volume equation would be wrong. You're missing the height. What would it be?