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|dw:1436828452402:dw|

if we make the cuts and fold up the box, we get something like this
|dw:1436828568511:dw|

Okay. What next? I know Volume would be lwh --- so x(20-2x)(60-2x)?

correct

So, then what?

ok so if you graph x(20-2x)(60-2x) with something like desmos, you get this (see attached)

Okay?

So 2525 is the max volume?

desmos is saying that the max point is (4.514, 2525)
so x = 4.514 and the max volume is 2525
yes

Thank you!

no problem

So what if you wanted to work it out by hand? Just wondering..

to do so by hand, you would need to know calculus (specifically, derivatives)

I do haha. I did it originally using derivatives and my teacher yelled at me and marked it wrong

such a strange thing to be yelled at for lol

I'm actually in calculus and my sister taught me derivatives

ok let's use derivatives then

Ya, I got that far. Then quadratic?

Then plug them back in for the y

because 0 < x < 10, we can ignore x = 22.15250437

I find it extremely frightening that you just completed the problem so quickly going the long way

I've had lots of practice

Maybe one day I will be able to do that

you will with enough practice

Again, thank you for your help

no problem