1. ## Beginner optimization problem

I really feel like I'm going on the wrong track on this problem:

A rectangular piece of cardboard, $100 cm$ by $40 cm$, is going to be used to make a rectangular box with an open top by cutting congruent squares from the corners. Calculate the dimensions for a box with the largest volume.

What I did so far was find height to either $h=\frac{100-y}{2}$ or $h=\frac{40-x}{2}$. Is that correct?

Also, area is $A=xy+2hy+2hx$?

What would I do next?

2. Think, if x and y are not equal what happens to the open box when you "put it together"?

3. Originally Posted by eulcer
Think, if x and y are not equal what happens to the open box when you "put it together"?
Erm, it becomes a rectangular box? Not sure what you're asking D:

4. Originally Posted by youngb11
Erm, it becomes a rectangular box? Not sure what you're asking D:
Sorry, I wrote out a long response and my cpu cut out on me.
Simply said the cut corners need to be squares for the opened box to be an opened box. If not the height will be different on two of the sides.

5. Our variables meant different things, so I'm sorry I made things harder for you.
Y is the length left after you cut the two corners from the 100 side and x is the length after you cut from 40. '
Nonetheless h will be equal to h, no?
So x=y-60.
Now you can put the Volume in terms of x or y solely and solve by using derivatives and max. points.

6. Originally Posted by youngb11
A rectangular piece of cardboard, $100 cm$ by $40 cm$, is going to be used to make a rectangular box with an open top by cutting congruent squares from the corners. Calculate the dimensions for a box with the largest volume.