Question

D Question 16 15 pts A simple mode-choice model is estimated from data in Blacksburg to predict the probabilities that travelers will select various modes of transportation to get to a new shopping area in Christiansburg, the Super Fun Times Mall. The utility functions are estimated as: Ucar- 2.5-0.25 (costcar)-0.03 (travel time ar UBlacksburg Transit (BT 0.25 (costgr)- 0.02 (travel timegT) Ubicycle -0.03 (travel time bicycla) where cost is in dollars and the travel time is in minutes. The cost of driving the automobile is $4.00 with a travel time of 25 minutes. The cost of taking Blacksburg Transit is $1.00 but is free for students with a travel time of 40 minutes. The travel time to ride a bicycle is 50 minutes. What is the probability that a student will take Blacksburg transit?

Answer 1

Ucar = 2.5-0.25*4-0.03*25=0.75

Ubt = -0.25*0 - 0.02*40 =-0.8 [ 0(free) for students ]

Ubicylcle = -0.03*50=-1.5

P(a student take Blacksburg transit) = e^0.8/(e^-0.75+e^0.8+e^1.5) = 0.309981