Question

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. if the cardboard is 17 in. long and 12 in. wide, find the dimensions of the box that will yield the maximum volume. (round your answers to two decimal places.)

Answer 1

The maximum value that could be reached would be about 211.05 cubic inches.

The initial measurements of the box are:
Length: 17
Width: 12
Height: 0

Right now, the volume is zero. However, if we let the height equal 0 (the amount of the cut out), we can write the following equation for the volume.

Volume = (17 - 2x)(12 - 2x)x

If you graph this, you will find a maximum value of 211.05, keeping in mind that the cut out must be less than 6.