We will use a logit model to study the time people depart from their houses. Assume $1000$

people are travelling from $A$ to $B.$ They work in $B$ and their job starts at $8\mathrm{.}00AM.$ They can

decide to depart at $7\mathrm{.}00,7\mathrm{.}15,$ or $7\mathrm{.}30.$ Because drivers run into different amounts of traffic

depending on their departure time, their travel times are not the same:

If they depart at $7\mathrm{.}00,$ it takes them $40$ minutes to arrive at $B.$

If they depart at $7\mathrm{.}15,$ it takes them $45$ minutes to arrive at $B.$

If they depart at $7\mathrm{.}30,$ it takes them $35$ minutes to arrive at $B.$

The utility of departing at time $t$ is:

$U(t)=-0\mathrm{.}5*T_t-1*E{A}_t-2*L{A}_t$

Where $T_t$ is the travel time, $E{A}_t$ is how early they arrive $("$Early Arrival"$),$ and $L{A}_t$ is how late

they arrive $("$Late Arrival"$),$ where all the units are in minutes. Assuming a logit model of

parameter $0\mathrm{.}5,$ predict how many users will depart at every time.