Posted by **Jemima** on Thursday, July 19, 2012 at 11:44pm.

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?

- calc -
**Reiny**, Friday, July 20, 2012 at 9:26am
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.

- Precalc -
**Gwen**, Sunday, October 11, 2015 at 6:55pm
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

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