Find the dimensions of the enclosure that is most economical to construct?
April 11, 2010 - 9:08 am
A fence is to be built to enclose a rectangular area of 240 square feet. The fence along three sides is to be made of material that costs 5 dollars per foot, and the material for the fourth side costs 16 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
A = W L = 240
P = 2W + 2L
cost = (5+5)W + 5L + 16L
but W = 240/L (from A)
cost = 2400/L + 21L
cost’(L) = -2400/L^2 + 21 = 0 at the optimum L
21L^2 = 2400
L = sqrt(2400/21)
April 11th, 2010 at 2:34 pm
A = W L = 240
P = 2W + 2L
cost = (5+5)W + 5L + 16L
but W = 240/L (from A)
cost = 2400/L + 21L
cost’(L) = -2400/L^2 + 21 = 0 at the optimum L
21L^2 = 2400
L = sqrt(2400/21)
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