An open rectangular box is to be constructed from a piece of cardboard a=25cm by b=46cm, by cutting squares of length x from each corner and folding up the sides. What should by equation be for this?

Question

An open rectangular box is to be constructed from a piece of cardboard a=25cm by b=46cm,  by cutting squares of length x from each corner and folding up the sides. What should by equation be for this?

anonymous · Answer

*my, not by

anonymous · Answer

i bet this really means "what is the equation for the volume ?" yes?

anonymous · Answer

Yes

anonymous · Answer

should be 
$$V(x)=x(25-2x)(46-2x)$$

anonymous · Answer

Then what should I do?

anonymous · Answer

if you draw a picture it will be clear. now we want to maximize volume i bet
$$v(x)=4 x^3-142 x^2+1150 x$$
$$V'(z)= 2 (6 x^2-142 x+575)$$ set equal zero and solve, get 
$$x= \frac{71-\sqrt{1591}}{6}$$

anonymous · Answer

you did not ask that question but i am guessing that it is what the question is after

anonymous · Answer

wait, I don't understand why it isn't V(z)=2(2x^3-71x^2+575x)