find the dimensions of the box that will yield the maximum volume.

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 14 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

v=x(14-2x)(12-2x)=168x -52x^2+4x^3

v' = 12x^2 -104x +168=0

3x^2 -26x +42=0

(3x-8)(x-6)=0

x=8/3= 2.67 inches by 8.67 inches by 6.67 inches

max v = (8/3)(26/3)(20/3)= 520(8)/27= 4160/27 in^3

=about 154.07 in^3