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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

Economics (MindTap Course List)
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter25: Government And Product Markets: Antitrust And Regulation
Section25.2: Regulation
Problem 1ST
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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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