Page 96 - How To Solve Word Problems In Calculus

from one end and used to form the rectangle. The remaining
2
10 inches is used to construct the square.
7
EXAMPLE 5
An open box is formed by cutting squares of equal size from
the corners of a 24 by 15-inch piece of sheet metal and folding
up the sides. Determine the size of the cutout that maximizes
the volume of the box.

Solution
Step1
Let x represent the size of the cutout.

x x
x x

15" w

x x
x x
l
24"

Step2
V = l × w × h

Step3
l = 24 − 2x

w = 15 − 2x

h = x

From step 2,
V(x) = (24 − 2x)(15 − 2x)(x)

15
2
3
= 4x − 78x + 360x 0 ≤ x ≤
2

15
if x > , w becomes negative
2
83