Chapter 3.3, Problem 59E

To determine

(a)

The mathematical proof of the statement stating that the total revenue earned by the Couture clothing chain will increase at the rate of

$\frac{dR}{dt}=5S(t)+10,000N(t)$ if R(t) is the revenue per month earned by the Couture clothing chain at time t, N(t) is the number of stores and S(t) is the average revenure per store per month.

To determine

(b)

The value of $\frac{dR}{dt}$ at time t = 0

To determine

(c)

The only leg of the campaign that Couture clothing should implement for the revenue to grow most rapidly