# Optimization finding expression

1. Mar 26, 2006

### Hollysmoke

I drew out that diagram but I think I might be wrong. The question is:

Tom makes an open box from a rectangular piece of metal by cutting equal squares from the four corners and turning up the sides. The piece of metal measures 60 x 100 cm. What are the dimensions of the box with the maximum volume?

2. Mar 26, 2006

### Hollysmoke

I wrote A=(60-2x)(100-2y)

3. Mar 26, 2006

### PPonte

$$V = l.w.h$$
$$V = (100-2y)(60-2x)(y)$$

If he cut squares from the four corners, then y = x.

$$V = (100-2x)(60-2x)(x)$$

Find the maximum value of V for positive values of x and you have your solution.

4. Mar 26, 2006

### Hollysmoke

OHH...Right. Okay, thank you!

5. Mar 26, 2006

### Hollysmoke

Okay this is strange...
After expanding and simplifying, I get
V=4x^3-320x^2+6000x

I differentiate that too
V'=12x^2-640x+6000

but I'm not getting the answer in the textbook. What am I doing wrong?

6. Mar 26, 2006

### Hollysmoke

nvm...I should have differentiated using the product rule D8

7. Mar 26, 2006