Answer
The largest monthly profit is ${{\$}} 845$ per month,
when the log-on fee is ${{\$}} 1.25$.
Work Step by Step
$P=R-C$
$P=-560x^{2}+1400x-30$.
The graph of P(x) is a parabola opening down.
The largest monthly profit occurs at the vertex, when
$x=-b/(2a)=-\displaystyle \frac{1400}{-2\times 560}= {{\$}} 1.25$
The corresponding profit is
$P=-560(1.25)^{2}+1400(1.25)-30 ={{\$}} 845$ per month.
