Chapter 8 - Review - Page 532: 55

210 and 210

$x+y=420$ $x*y=z$ $x+y=420$ $x+y-y=420-y$ $x=420-y$ $x*y=z$ $(420-y)*y=z$ $420*y-y^2=z$ $-y^2+420y=z$ We want the maximum value, so we are looking for the vertex of this graph. $a=-1$, $b=420$, $c=0$ $y=-b/2a$ $y=-420/2*-1$ $y=-420/-2$ $y=210$ $x+y=420$ $x+210=420$ $x+210-210=420-210$ $x=210$