Question

A work-mode-choice model is developed from data acquired in the field in order to determine the probabilities of individual travelers selecting various modes. The mode choices include automobile drive-alone (DL), automobile shared-ride (SR), and bus (B). The utility functions are estimated as follows:

UDL = 2.6 - 0.3 (costDL) - 0.02 (travel timeDL)
USR = 0.7 - 0.3 (costSR) - 0.04 (travel timeSR)
UB = -0.3 (costB) - 0.01 (travel timeB)
where cost is in dollars and time is in minutes. The cost of driving an automobile is exist5.50 with a travel time of 21 minutes, while the bus fare is exist1.25 with a travel time of 27 minutes. How many people will use the shared-ride mode from a community of 4500 workers, assuming the shared-ride option always consists of three individuals sharing costs equally?
a. 314
b. 828
c. 866
d. 2805

Answer 1

b. 828

Step-by-step explanation:

UDL = 2.6 - 0.3 [5.5] - 0.02 [ 21 ] = 0.53

USR = 0.7 - 0.3 [5.5 / 2 ] - 0.04 [ 21 ] = -0.69

UB = -0.3 [ 1.25 ] - 0.01 = -0.645

Psr =
`(e^(-0.53) )/(e^(-0.53) + e^(-0.69) + e^(-0.645) )`

Solving the equation we get 0.184.

Number of people who will take shared ride is:

0.184 * 4500 = 828 approximately.