A postal service will accept packages only if the length plus girth is no more t

Question

A postal service will accept packages only if the length plus girth is no more than 216 inches. (See the figure.) Assuming that the front face of the package (as shown in the figure) is square, what is the largest volume package that the postal service will accept?
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A postal service will accept packages only if the length plus girth is no more than 216 inches. (See the figure.) Assuming that the front face of the package (as shown in the figure) is square, what is the largest volume package that the postal service will accept?

Explanation / Answer

l+4a = 216 so l = 216-4a

volume = l*a^2

= (216-4a)*a^2

differentiating with respect to a we get

432a - 12a^2 = 0

a = 36 so l 72

largest volume = 72*36*36 = 93312 in^3

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