QUESTION 3 (30 MARKS) 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) 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: 1 F = W The profit function P for each shopping center is defined to be: P=10C-5000 A where 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 (b) Determine the profit P for each shopping center using the number of customers determined in (a). (c) Assume that M maintains its attractiveness at 2 units, while N decides to maximize its profit. Using the profit function defined earlier, (1) How should N modify its attractiveness so as to maximize its profit? (ii) What are the resultant profits for M and N