Calculus with Applications (10th Edition)

a. $m=2.15$; b. $187.5$ books; c. $545$ books
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$C(x)=R(x)2.15x+525=4.95x2.8x=525x=187.5$c. Let$P(x)=1000$in the equation$P(x)=4.95x-(2.15x+525)1525=2.8xx \approx 544.6 \approx 545\$