A parcel delivery service will deliver a package only if the length plus the girth (distance around, taken perpendicular to the length) does not exceed 116 inches. Find the maximum volume of a rectangular box with square ends that satisfies the delivery company's requirements.

Question

Mathematics

Harold Zhang

23 November, 19:53

A parcel delivery service will deliver a package only if the length plus the girth (distance around, taken perpendicular to the length) does not exceed 116 inches. Find the maximum volume of a rectangular box with square ends that satisfies the delivery company's requirements.

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Answers (1)

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Emilio Mccoy · Answer 1

14449 inches^3

Step-by-step explanation:

length+girth=116 inches

w + 4x = 116

volume=x^2*w

w=116-4x

V=x^2 * (116-4x)

for max value, dv/dx=0

dv/dx = 232x-12x^2

232x-12x^2=0

x=19.3333

w=116-4 (19.33)

=38.67

V=19.33^2*38.67=14449 inches^3