Question 813199
2L + 2w = 3000
L + w = 1500
L = 1500 - w
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A = Lw
A = (1500 - w)w
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Area is now a quadratic function of width (w):
A(w) = -ww + 1500w + 0
A(w) = (-1)w^2 + 1500w + 0
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the above quadratic equation is in standard form, with a=-1, b=1500, and c=0
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to find the maximum area A(w), plug this:
-1 1500 0
into this: https://sooeet.com/math/quadratic-equation-solver.php
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Answer 1:
the maximum point of the above quadratic equation is: ( 750, 562500 )
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so the maximum area that can be enclosed is: 562500 sq.ft. (the y-coordinate of the maximum point)
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now, to find the L and w dimensions of the maximum area, remember this equation from above:
A(w) = (-1)w^2 + 1500w + 0
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we used that eqn to maximize Area, but as a side effect we also got w for that max area, from the maximum point: ( w=750, A=562500 )
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Answer 2:
w for maximum area = 750
L for maximum area = 1500 - w = 1500 - 750 = 750
so the maximum area has dims: w=750, L=750
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