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January 2nd, 2017, 01:05 PM   #1
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maximum

of all numbers whose sum is 80 find the two that have the maximum product that is; maximise p=xy where x+y=80

I know the answer is 40 by just looking at it but is there a algebraically way to di it
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January 2nd, 2017, 01:19 PM   #2
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$x+y = 80 \implies y = 80-x$

$xy = p = x(80-x) = 80x-x^2$

the graph of $p$ is an inverted parabola with a maximum value at its vertex ... how do you find the vertex and determine the maximum for $p$ ?
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