Answer
a. $m=2.15$;
b. $187.5$ books;
c. $545$ books
Work Step by Step
a. The total cost $C(x)$ in dollars of producing and selling $x$ units is given by
$C(x)=mx+b$
with $x=1000, b=525, mx+b=2675$
we have $C(1000)=m(1000)+525=2675$
$1000m=2150$
$m=2.15$
b. Since $R(x)=px$ and $p=\$4.95$,
$R(x)=4.95x$
Substituting for $R(x)$ and $C(x)$ in the equation $R(x)=C(x)$ gives
$C(x)=R(x)$
$2.15x+525=4.95x$
$2.8x=525$
$x=187.5$
c. Let $P(x)=1000$ in the equation $P(x)=4.95x-(2.15x+525)$
$1525=2.8x$
$x \approx 544.6 \approx 545$
