# Maximization problem

1. Nov 19, 2006

### Apost8

OK, I've been killing myself over this one problem and I just cannot seem to get it. :grumpy: I know it's probably a lot easier than I'm making it out to be. If anyone can give me a little help I would really appreciate it. Here's the question:

If 1200cm^2 of material is available to make a box with a square base and an open top, what is the box's larget possible volume?

So far, I'm guessing that since the base of the box is to be square and there's an open top, the area of the box = x^2 + 4xy = 1200 and the volume = (x^2)y.

I know at some point I'll need to differentiate and find the maximum of the function, but, I'm sort of floundering at this point. Thanks in advance.

2. Nov 19, 2006

### Hootenanny

Staff Emeritus
Okay so you know have two functions, one of which you wish to maximise (i.e. the volume). Using your first equation can you write a function for y in terms of x?

3. Nov 19, 2006

### Apost8

So, if I solve the first equation for y, I get y = (1200-x^2)/4x Is this correct?

4. Nov 19, 2006

### Hootenanny

Staff Emeritus
Indeed it is. Can you guess what you need to do with this result?

5. Nov 19, 2006

### Apost8

Plug that into my equation for volume, differentiate, and find the max?

6. Nov 19, 2006

### Hootenanny

Staff Emeritus
Sounds good to me.

7. Nov 19, 2006

### Apost8

Got it. That wasn't so hard, jeez. Thanks for the help! :)

8. Nov 19, 2006

### Hootenanny

Staff Emeritus
No worries . Don't forget to verify that your answer is a maximum and is meaningful.

Last edited: Nov 19, 2006