Calculus Optimization Word Problems

An open box is made by cutting and folding a 10x10 inch square of cardboard as shown below. Find the maximum volume the open box can attain by altering the length of cuts, x.

A dudebro has 500 feet of fencing to make a pig pen along a barn as shown below. Find the maximum area.

Find two non-negative numbers, x and y, whose sum is 9 with a maximum product of x and the square of y, $p(x,y) = xy^2$

Find the maximum value of $f(x) = xe^{-x}$ on $(-\infty, \infty)$