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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 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

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
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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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