Question

C5: Problem 6 Previous Problem Problem List Next Problem (1 point) Your task is to design a rectangular industrial warehouse consisting of three separate spaces of equal size. The wall materials cost $87 per linear foot and your company has allocated $93960 for those walls. 1) The dimensions which use all of the budget and maximize total area are length L (include units in this answer) width W (units needed here too) 2) Each of the three (equal size) compartments has area (include units)

Answer 1

1)

total cost =87(L+L+W+W+W+W)
=>total cost =87(2L+4W)

allocated $ 93960

=>87(2L+4W)=93960
=>174(L+2W)=93960
=>L+2W=540
=>L=540-2W

total area ,A(L,W)=LW
=>A(W)=(540-2W)W
=>A(W)=-2W²+540W
=>A'(W)=-2(2)W^2-1+540(1)
=>A'(W)=-4W+540
=>A''(W)=-4(1)+0
=>A''(W)=-4

for maximum total area ,A'(W)=0,A"(W)<0

=>-4W+540=0
=>4W=540
=>W=135

A''(135)=-4
=>A''(135)<0

L=540-2W ,W=135
=>L=540-2(135)
=>L=540-270
=>L=270

therefore the dimensions for the maximum total area are
length L=270 feet
width W =135 feet

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2)

area of each of 3 compartments

LW 270 * 135 12150

each of 3 compartments has area of  12150 square feet

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