Question 1051181: Please help me how to solve this problem.Thanks.
Ramon wants to fence in a rectangular portion of his back yard against the back of his garage for a vegetable garden. He plans to use 68 feet of fence, and needs fence on only three sides. Find the maximum area he can enclose. (Hint: The lengths of the 3 fenced sides of the rectangle must add up to 68.)
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! we know that
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1) l + 2w = 68, where l is the length and w is the width of the rectangle
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also
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2) l * w = Area of the rectangle
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solve equation 1) for l
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l = 68 - 2w
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substitute for l in equation 2)
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w * (68 - 2w) = Area
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-2w^2 + 68w = Area
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The equation for the Area in terms of w is a parabola that opens downward, so
we know that w is maximum at the vertex
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To find w, we take the first derivative of the equation for Area, then set it
equal to 0 and solve for w
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-4w + 68 = 0
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-4w = -68
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w = 17
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l = 68 -2(17) = 34
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Maximum Area is 34 * 17 = 578 square feet
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