The revenue per month earned by the Couture clothing chain at time t is R(t) = N(t)S (t), where N(t) is the number of stores and S (t) is average revenue per store per month. Couture embarks on a two-part campaign: (A) to build new stores at a rate of five stores per month, and (B) to use advertising to increase average revenue per store at a rate of $10,000 per month. Assume that N(0) = 50 and S (0) = $150,000.
(a) Show that total revenue will increase at the rate

Note that the two terms in the Product Rule correspond to the separate effects of increasing the number of stores on the one hand and the average revenue per store on the other.

(b)

(c) If Couture can implement only one leg (A or B) of its expansion at t = 0, which choice will grow revenue most rapidly?

Transcribed Image Text:

dR dt 5S (t) + 10,000N(t)