A Rectangular Package To Be Sent By A Postal Service Can Have A Maximum Combined Length And Girth

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A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross-section) of 108 inches. Find the dimensions of the package of maximum volume that can be sent. (Assume the cross-section is square.)

Answer

108 – 4x*y

108-4x=y

There is a max at x = 18 because A'(x) = 0. There is a min at x = 0.

Result

X=18

y(x)=108-4(18)=36

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