Answer:
hi your question is lacking the required data here is the complete question
where cost is in dollars and time is in minutes. The cost of driving an automobile is $5.50 with a travel time of 21 minutes, while the bus fare is $1.25 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
The mode choices includes automobile drive alone ( Dl ), automobile shared ride ( Sr ), bus ( b )
The utility functions are estimated as
UDL = 2.6 - 0.3 (cost dl) - 0.02 (travel time dl )
USR = 0.7 - 0.3 ( cost Sr ) - 0.04 ( travel time Sr )
UB = 0 - 0.3 ( cost b ) - 0.01 ( travel time b )
Answer options : a) 866 b) 2805 c)828 d)314
Answer : approximately 828 people would use the shared ride option ( c )
Explanation:
Inputting the values into the estimated utility functions
UDL ( drive alone ) = 2.6 - 0.3 ( 5.5 ) - 0.02 ( 21 ) = 0.53
USR ( shared ride ) = 0.7 - 0.3 ( 5.5 ÷ 2 ) - 0.04 ( 21 ) = -0.69
UB ( bus ride ) = 0 - 0.3 ( 1.25 ) - 0.01 ( 27 ) = -0.645
In order to get the probability of the people that would use the shared ride mode we apply the logit model formulation
Psr = [tex]\frac{e^{-0.69} }{e^{0.53}+ e^{-0.69}+e^{-0.645} }[/tex]
hence Psr = 0.184
The number of people that would probably take the shared ride option would be calculated as:
0.184 * 4500 = 828
