Solve the problem
-A rectangular piece of cardboard measuring 19 inches by 28 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent
The length of a side of each such square. For what value of x will the volume be a maximum? If
Necessary, round to 2 decimal places.
A) 14.66 in.
B) 23.92 in.
C) 3.71 in.
D) 11.96 in.

Question

Quizplus · Accepted Answer

The volume of the box, V, can be expressed as a function of x: V = x(19 - 2x)(28 - 2x). To find the value of x that maximizes the volume, we differentiate this function with respect to x and set the derivative equal to zero to solve for x. This yields a maximum volume at x ≈ 3.71 inches.

Solve the Problem -A Rectangular Piece of Cardboard Measuring 19 Inches by 28