Problem 3 (20 points + 2 Bonus points ) A mobility service company decides to start operation in a new city. The company has hired you to help determine the viability of its business in the city. You have estimated a logit model with the two modes available (DL-drive alone, B-bus) with the following utility functions: UDL=2.3 -0.2(costou) -0.03(travel timepu) Ug = -0.2(costo)-0.01(travel times) where cost is in dollars and travel time in minutes. Between a residential area and a commercial complex 4,000 trips are generated. You have identified this origin-destination pair as the most attractive market for the company and collected the following information for the existing modes: Variable Travel time (min) Cost (in %) Mode Drive Alone 20 6 Bus 25 1 Suppose that you have estimated the utility function for the new mobility service MS as: UMS = 0.8 -0.2(costs) - 0.03(total times) Where, total time includes both travel time and waiting time. Answer the following: i. How many trips are made by each mode (drive alone and bus) before introducing the new mobility service option? (4 points) ii. Assume that the travel time for the new option will be 20 min and waiting time for each ride will be 5 min and a customer has to pay $5.00 for each ride. How many trips will be served by the new mobility service? (4 points) iii. If the company has to pay a service tax of $1,500 per day for operating in the city and a flat $2.00 for each ride to the drivers, will it be a profitable operation for the company? (4 points) iv. If the company wants to capture 25% of the market share, what price per ride should it offer to its customers? (4 points) v. Determine the ratio of the probability of choosing drive alone to that of buses ) before and after introducing the new mobility service. (4 points) What property of logit model is responsible for these values? (2 Bonus points)