by cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, the cardboard may be turned into an open box. if the cardboard is 16 inches long and 10 inches wide, find the dimensions of the box that will yield the max volume. what is the max volume?

Question

Reiny · Answer

let each side of the square to be cut out be x inches
length of base = 16-2x
width of base = 10-2x
height of box = x inches

V = x(16-2x)(10-2x) , where 0 < x < 5

I would now expand that to get a cubic
take the derivative, which is a quadratic,
set the derivative equal to zero and solve for x

Very straight forward question, most Calculus texts use that question as an introduction to optimization.

Gwen · Answer

Two Congruent squares are removed from one end of a rectangle 10 inch by 20 inch piece of cardboard. Two congruent rectangles are removed from the other end Determine the value of x so that the resulting box has maximum volume