A dairy farmer plans to enclose a rectangular pasture adjacent to a river. To provide enough grass for the herd, the pasture must contain 180,000 square meters. No fencing is required along the river. What dimensions will use the smallest amount of fencing?
Area is given as:
A = L*W = 180000m
3-sided fencing length is:
F = L 2W
F = (A/W) 2W
Find minimum fencing by setting derivative =0
dF/dW = 2-A/W = 0
W = (A/2) = 300m
L = A/W = 600m
F = L 2W = 1200m
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