PP Section 4.5 - MaximumandMinimum Problems TheProblem...

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    Maximum and Minimum  Problems
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    The Problem Want:  to solve optimization problems An optimization problem wants to find the maximum of  minimum value of a function. What we know:  A quadratic function has a maximum or a  minimum value at its vertex. To do:  Find the vertex of a quadratic function and  interpret the result in the context of the word problem.
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    Example A farmer wants to enclose a rectangular pen on three  sides with 1,000 ft. of fencing. The fourth side is  bordered by a straight river. Find the dimensions of the  pen that maximize the area. River x x y Given:  2x + y = 1000 Area = xy Solving for y:  y = 1000 – 2x Hence the area is:  A(x) = x(1000 – 2x)
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    x x x x x A 1000 2 ) 2 1000 ( ) ( 2 + - = - = We have a quadratic function with a < 0, so the  parabola opens down. Hence there is a maximum value at the vertex.
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PP Section 4.5 - MaximumandMinimum Problems TheProblem...

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