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Two shopping centers M and N are competing for customers from two residential zones X and Y. For shopping trips, the productions per day (or home-based trip ends) of the two zones are: Zone Productions per day X 2000 Y 1000 For the shopping centers, their current attractiveness is: Shopping center Attractiveness (4) 2 M N 4 The skim table W between the residential zones and shopping centers is as follows: From to M N X 10 10 Y 20 20 All socioeconomic factors equal one and the friction factor F is given by: F=1 W The profit function P for each shopping center is defined to be: P=10C-5000A where C is the number of customers going to the shopping center and A is the shopping center's attractiveness. Determine the number of customers from X and Y to M and N, respectively. Express your answers in a table format, as in the following. From To M N X Y Determine the profit P for each shopping center using the number of customers determined in (a). Assume that M maintains its attractiveness at 2 units, while N decides to maximize its profit. Using the profit function defined earlier, (i) How should N modify its attractiveness so as to maximize its profit? (ii) What are the resultant profits for M and N? (b) (c)

Two shopping centers M and N are competing for customers from two residential zones X and Y. For shopping trips, the productions per day (or home-based trip ends) of the two zones are: Zone Productions per day X 2000 Y 1000 For the shopping centers, their current attractiveness is: Shopping center Attractiveness (4) 2 M N 4 The skim table W between the residential zones and shopping centers is as follows: From to M N X 10 10 Y 20 20 All socioeconomic factors equal one and the friction factor F is given by: F=1 W The profit function P for each shopping center is defined to be: P=10C-5000A where C is the number of customers going to the shopping center and A is the shopping center's attractiveness. Determine the number of customers from X and Y to M and N, respectively. Express your answers in a table format, as in the following. From To M N X Y Determine the profit P for each shopping center using the number of customers determined in (a). Assume that M maintains its attractiveness at 2 units, while N decides to maximize its profit. Using the profit function defined earlier, (i) How should N modify its attractiveness so as to maximize its profit? (ii) What are the resultant profits for M and N? (b) (c)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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➜ ☺ T Two shopping centers M and N are competing for customers from two residential zones X and Y. For shopping trips, the productions per day (or home-based trip ends) of the two zones are: Zone Productions per day X 2000 Y 1000 For the shopping centers, their current attractiveness is: Shopping center Attractiveness (A) M 2 4 N The skim table W between the residential zones and shopping centers is as follows: From to M N X 10 10 Y 20 20 All socioeconomic factors equal one and the friction factor F is given by: 1 F= W The profit function P for each shopping center is defined to be: P=10C-5000 A where C is the number of customers going to the shopping center and A is the shopping center's attractiveness. (a) Determine the number of customers from X and Y to M and N, respectively. Express your answers in a table format, as in the following. From To M N X Y Determine the profit P for each shopping center using the number of customers determined in (a). Assume that M maintains its attractiveness at 2 units, while N decides to maximize its profit. Using the profit function defined earlier, (i) How should N modify its attractiveness so as to maximize its profit? (ii) What are the resultant profits for M and N? Filters Add a caption... C > My group × (b) (c)
Transcribed Image Text:➜ ☺ T Two shopping centers M and N are competing for customers from two residential zones X and Y. For shopping trips, the productions per day (or home-based trip ends) of the two zones are: Zone Productions per day X 2000 Y 1000 For the shopping centers, their current attractiveness is: Shopping center Attractiveness (A) M 2 4 N The skim table W between the residential zones and shopping centers is as follows: From to M N X 10 10 Y 20 20 All socioeconomic factors equal one and the friction factor F is given by: 1 F= W The profit function P for each shopping center is defined to be: P=10C-5000 A where C is the number of customers going to the shopping center and A is the shopping center's attractiveness. (a) Determine the number of customers from X and Y to M and N, respectively. Express your answers in a table format, as in the following. From To M N X Y Determine the profit P for each shopping center using the number of customers determined in (a). Assume that M maintains its attractiveness at 2 units, while N decides to maximize its profit. Using the profit function defined earlier, (i) How should N modify its attractiveness so as to maximize its profit? (ii) What are the resultant profits for M and N? Filters Add a caption... C > My group × (b) (c)
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