Note that the two terms in the Product Rule correspond to the separate effects of increasing the number of stores and the average revenue per store. dR (b) Calculate dt -0 (c) If Couture can implement only one leg (A or B) of its expansion at ! = 0, which choice will grow revenue most rapidly? %3D The revenue per month eamed 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 dR 5S(t)+10,000N (t) dt

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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Note that the two terms in the Product Rule correspond to the separate
effects of increasing the number of stores and the average revenue per
store.
dR
(b) Calculate
dt -0
(c) If Couture can implement only one leg (A or B) of its expansion at
! = 0, which choice will grow revenue most rapidly?
%3D
Transcribed Image Text:Note that the two terms in the Product Rule correspond to the separate effects of increasing the number of stores and the average revenue per store. dR (b) Calculate dt -0 (c) If Couture can implement only one leg (A or B) of its expansion at ! = 0, which choice will grow revenue most rapidly? %3D
The revenue per month eamed 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
dR
5S(t)+10,000N (t)
dt
Transcribed Image Text:The revenue per month eamed 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 dR 5S(t)+10,000N (t) dt
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