SOLUTION: bob has 3000 ft of fence to build 4 adjacent pens. what is x and y? what is the maximum area he can obtain?

Question 175432: bob has 3000 ft of fence to build 4 adjacent pens. what is x and y? what is the maximum area he can obtain?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
bob has 3000 ft of fence to build 4 adjacent pens. what is x and y? what is the maximum area he can obtain?
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Draw the adjacent pens as a rectangle with base and top of y and height of x.
Notice there are 5 vertical pieces needed to construct four pens.
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Fence Equation: 5x + 2y = 3000
Area = xy
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Solve 1st for y: y = (-5/2)x + 1500
Substitute into the Area Equation:
A(x) = x[(-5/2)x+1500]
A(x) = (-5/2)x^2 + 1500x
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Maximum Area occurs when x = -b/2a = -1500/(-5) = 300
If x = 300 y = (-5/2)(300) + 1500 = 750
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Maximum area = xy = 300*750 = 225000 sq. ft.
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Cheers,
Stan H.
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