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a delivery company requires that any box delivered must have a length plus girth​ (distance around) totaling no more than 120 inches. find the dimensions of the box with maximum volume that can be sent.

Answer :

the dimensions of the box is length 20 and width 40inches with maximum volume that can be sent. is V = 16000 inches ^3

length + girth=116 inches

w + 4x= 120

volume=x^2*w

w=120-4x

V=x^2* (120-4x)

for max value, dv/dx=0

dv/dx= 240x-12x^2

240x-12x^2=0

20-x=0

x=20

w=120-4(20)

=40

V=20^2*40==16000inches^3

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