Question

An open-top box is being designed by cutting a corner piece out of a 16" by 14" piece of metal and folding the sides upwards. The designer wants to maximize the volume of this box. Enter the maximum volume of this box (rounded to the nearest cubic inch). in3

Answer 1

The strip of 16 by 14 inches.

Let x be the corner of the square cut

Then the box would have height as x, length 16-2x and width 14-2x

Hence volume =

Use derivative to test to find x for maximum volume

V'(x) =

v"(x) =

Equate first derivative to 0

Solutions are

x= 2.483 and x = 7.517

Practically cutting more than 7 inches is not possible from 14 inches dimention

Hence 2.483 is the side of square and maximum volume

= 247.508

Explanation:

Hope this helps!