An open box is to be made out of a 10-inch by 16-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

Question

Dimensions of the bottom of the box:

Answer 1

let each cut-out have sides of x inches each

length of box = 16-2x
width of box = 10-2x , where x < 5
height of box = x

volume = V = x(16-2x)(10-2x)

expand, take derivative,
set derivative, which is a quadratic, equal to zero and solve.
Make sure you take the value between 0 and 5