Problem $2(12$ points$)$

On the evening of May $8,$ Taylor Swift is scheduled to perform a concert at the GW

Charles E$.$ Smith Center. The District Department of Transportation is tasked with

estimating the travel demand from Rosslyn to Foggy Bottom for the concert on this

specific day during rush hours.

$[$Trip Generation$]$ A simple linear regression model is estimated for the recreational

trip generation in the evening peak hour. The model is

Number of peak$-$hour concert trips per household

$=0\mathrm{.}2+0\mathrm{.}003($household annual income in thousand dollars$)$

$+0\mathrm{.}1($number of youngsters in the household$)$

Suppose $10,000$ households in total in Rosslyn, with $2,000,5,000,$ and $3,000$ in type I, II

and III:

Predict the total number of concert trips from Rosslyn to Foggy Bottom in the evening

peak hour.

$[$Mode Choices$]$ All concert trips are made either by auto or metro. A logit model

estimation is made, and three factors were found to influence the mode choice: $(1)$ travel

time, in minutes $($coefficient $=-0\mathrm{.}1)$; $(2)$ parking fee needed, in US dollar $($coefficient $=$

$-0\mathrm{.}2)$; and $(3)$ tolls into DC$,$ in dollars $($coefficient $=-0\mathrm{.}2).$ The specific values of the two

modes in each aspect are as follows,

Determine the numbers of trips using auto and metro, respectively.