Question #286100

A delivery company accepts only rectangular boxes the sum of whose length and the perimeter of a cross-section does not exceed 108 inches. Find the dimensions of an acceptable box of largest volume. 


1
Expert's answer
2022-01-10T15:27:55-0500

L+4S=108

L=108-4S

v=s2Lv=s2(108−4s)v=108s2−4s3v′=216s−12s20=216s−12s2s=0,s=18then,L=108−4(18)L=36.v=s2L,v=182(36),v=11664in3v=s^2L\\ v=s^2(108-4s)\\ v=108s^2-4s^3\\ v'=216s-12s^2\\ 0=216s-12s^2\\ s=0,s=18\\ then, L=108-4(18)\\ L=36.\\ v=s^2L, v= 18^2(36),\\ v=11664in^3


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