Answer
a) $10,000N(t)+5S(t)$
b) $1,250,000$
c) increase the number of stores by 5 per month
Work Step by Step
a)
$\frac{dR}{dt}$ = $N(t)S'(t)+N'(t)S(t)$
N'(t) = 5
S'(t) = 10,000
so
$\frac{dR}{dt}$ = $10,000N(t)+5S(t)$
b)
$\frac{dR}{dt}|_{t=0}$ = $10,000N(0)+5S(0)$
N(0) = 50
S(0) = 150,000
so
$\frac{dR}{dt}|_{t=0}$ = $(10,000\times50)+(5\times150,000)$
$\frac{dR}{dt}|_{t=0}$ = $1,250,000$
c)
term 5S(0) is larger than the term10,000N(0) so
increase the number of stores by 5 per month grow revenue most rapidly
