Find the Dimensions of the garden that minimize the cost?
A landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $30/ft and on the other three sides by a metal fence costing $10/ft. If the area of the garden is 1,200 ft2, find the dimensions of the garden that minimize the cost. (Round to three decimal places.)
what is the length of brick wall?
what is the length of side adjacent to brick wall?
A = L * W
P = 2 L + 2W
A = 1200 = L W
L = 1200/W
Cost C = 30 L + 10( L + 2 W)
C = 40 L + 20 W
C = 40 (1200/W) + 20 W = 48000 / W + 20 W
dC/dW = -48000/W^2 + 20 = 0
W^2 = 2400
W = sqrt(2400) =20sqrt(6)
L = 1200/(20 sqrt(6)) = 10 sqrt(6)
L = 24.495 ft Brick wall
W = 48.990 ft adjacent wall
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