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

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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 =

hence Psr = 0.184

The number of people that would probably take the shared ride option would be calculated as:

0.184 * 4500 = 828

d. all of the above are true.