January 2nd, 2017, 01:05 PM  #1 
Member Joined: May 2016 From: Ireland Posts: 94 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, 01:19 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,549 Thanks: 1259 
$x+y = 80 \implies y = 80x$ $xy = p = x(80x) = 80xx^2$ 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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