SOLUTION: A farmer has 200 ft of fencing and wants to build three adjacent rectangular corrals. Determine the dimensions that should be used to maximize the area, and find the area of each i

Algebra ->  Functions -> SOLUTION: A farmer has 200 ft of fencing and wants to build three adjacent rectangular corrals. Determine the dimensions that should be used to maximize the area, and find the area of each i      Log On


   

Question 1051400: A farmer has 200 ft of fencing and wants to build three adjacent rectangular corrals. Determine the dimensions that should be used to maximize the area, and find the area of each individual corral.
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let w = width and l = length, then we have two formulas to consider
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1) 6l + 4w = 200
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2) Area = 3 * l * w
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solve equation 1) for w
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w = 50 - 1.5 * l
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substitute for w in equation 2
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Area = 3 * l * (50 - 1.5 * l)
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Area = -4.5l^2 + 150l
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take first derivative and set = 0 and solve for l
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-9l = -150
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l = 16.6667 use 16.6 feet
w = 50 - (1.5 * 16.6) = 25.1 use 25
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Area of each rectangular corral is 16.6 * 25 = 415 square feet
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Note that 6(16.6) + 4(25) = 199.6 feet
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