Question

According to postal regulations, a carton is classified as "oversized" if the sum of its height and girth (the perimeter of its base) exceeds 192 in. Find the dimensions of a carton (in inches) with square base that is not oversized and has maximum volume. (Enter the three dimensions as a comma-separated list.)

Answer 1

Answer:

Square base dimension = 15 inches

Maximum volume = 7200 inches^3

Step-by-step explanation:

V = x^2y ..... eq 1

Let the square base be x and the height y

Oversize formular is given by

Y + 4x = 92

Y= 92 - 4x .....eq 2

Put eq 2 into eq 1

V = x^2 ( 92 - 4x^3)

V= 92x^2 - 4x^3

Using derivatives

V= 184x - 12x^2

V'= 0 = 184x - 12x^2

X(184 -12x)

X=0

X = 184/12 = 15.33 approximately 15 inches

Maximum Volume = V= 92(15)^2 -5(15)^3

V= 92(225) - 4(3475)

V= 20700 - 13500

V= 7200 inches^3