Problem $1$

$3-6$ A calibration study resulted in the following utility equation for different modes in a

particular city:

$U_k=a_k-(0\mathrm{.}25)(x_1)-(0\mathrm{.}032)(x_2)-(0\mathrm{.}015)(x_3)-(0\mathrm{.}002)(x_4)$

where $a_k=$ mode specific constant

$x_1=$ access plus egress time in minutes

$x_2=$ waiting time in minutes

$x_3=$ line$-$haul time in minutes

$x_4=$ out$-$of$-$pocket cost in cents

For a particular origin$-$destination pair, the forecasted number of trips is $5,000.$ For this

particular trip, there are two modes available, bus and auto.

a$)$ If the characteristics of these two modes are as follows, how many trips will be taken

by bus? by car?

Assume that the mode specific constant is equal to $-0\mathrm{.}12$ for the automobile and $-0\mathrm{.}22$

for bus.

b$)$ Assume that a new mode, rapid transit, is to be introduced into the market between

these two zones. The characteristics of this new service are as follows:

$x_1=10,x_2=5,x_3=30,x_4=75$

Assume from experience in other cities that the mode specific constant for rapid transit

is $-0,41.$ What will be the modal shares of the $5,000$ trips between these two zones for all

three modes?

c$)$ Assume that the city council wants to increase ridership on transit in this new three$-$

mode system. They are considering one of two actions: lower the fare on bus and rapid tran$-$

sit to a flat $$0\mathrm{.}25$ for all trips, or place a surcharge of $$2\mathrm{.}00$ on all cars parking in these zones.

Which policy would you recommend to achieve the council's objective?