An open box is to be made out of a 12-inch by 18-inch piece by cutting out squares of equal size from the four corners and bending up the sides

Question

. Find the dimensions of the resulting box that has the largest volume dimensions??? Height??

Answer 1

A piece of cardboard is 12" x 18" and you cut squares of x" from each of the four corners. The length of the resulting open box will be 18 - 2x inches; the width will be 12 - 2x inches; the height will be x inches.

So the volume that you need to maximize is (18 - 2x)(12 - 2x)(x)

If you expand that you'll get V = 4x³ - 60x² + 216x.

Can find max value of V by taking 1st derivative and setting equal to zero and solve for x, or plot the graph on Desmos Graphing Calculator.