Problem $1$: Application of Mode Choice Binary Logit Model

The following equation was estimated in class. Let us assume it represents the utilities for different transportation modes for Villanova University community to travel to Philadelphia.

$U=-0\mathrm{.}095x_1-0\mathrm{.}238x_2$

Where

$x_1$ is total travel time in minutes

$x_2$ is total out$-$of$-$pocket cost in dollars

On December $9,$ VU Basketball Team will host UCLA in Wells Fargo Center. The University is working with SEPTA to analyze travel demand and make sure the transportation system can handle traffic effectively. Let us assume $5,000$ students plan to go to downtown Philadelphia during the Game Day. Between Villanova and Philadelphia, let us assume there are two alternative modes available, transit and auto. The attributes of these two modes are shown in the table below:

$\backslash$table$[[$Attributes$,x_1,x_2$