Example:

A city has a utility function for use in a logit model of the form

$U=-0\mathrm{.}075A-0\mathrm{.}05W-0\mathrm{.}04R-0\mathrm{.}02C$

where $A$ is the access time in minutes, $W$ is the waiting time in minutes, $R$ is the riding

time in minutes, and $C$ is the out$-$of$-$pocket cost in cents.

$($a$)$ What modal distribution would you expect, using the following values for A$,$ W$,$ R$,$ and

C$,$ for the four modes used in the city.

$($b$)$ The city is seriously thinking of subsidizing rail and bus by $50\%,$ encouraged biking

by constructing bike paths and thus reducing biking time by $20\%,$ and increasing auto

costs $($through higher parking charges$)$ by $10\%.$ What is likely to be the new modal

distribution with these charges?

The total number of trips from zone $i$ to zone $j$ is $4200.$ Currently all trips are made by car. Government

has two alternatives$-$ to introduce a train or a bus. The travel characteristics and respective coefficients

are given in table $9$:$5.$ Decide the best alternative in terms of trips carried.

Table $9$:$5$: Trip characteristics