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 January 2nd, 2017, 12:05 PM #1 Member   Joined: May 2016 From: Ireland Posts: 96 Thanks: 1 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
 January 2nd, 2017, 12:19 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,640 Thanks: 1319 $x+y = 80 \implies y = 80-x$ $xy = p = x(80-x) = 80x-x^2$ 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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