Problem $2$: Trip Distribution $3(25$ points$)$

You are asked to perform trip distribution for five origin$-$destination $($OD$)$ pairs for a certain analysis period using the Gravity model. The travel time skim matrix is provided in Table $3\mathrm{.}1,$ while the productions and attractions for each zone are given in Table $3\mathrm{.}2.$ The friction factor $F_1$ has the following form:

$F_{ij}=a*t_{ij}*exp(c*t_{ij})$

Where:

$a=150,b=-0\mathrm{.}85,c=-0\mathrm{.}125$

Note that before starting with trip distribution, you need to perform balancing for productions and attractions.

Perform only the initial iteration. Provide methodologies for each step, and show the results in a tabular form.

Table $21$: Zone$-$to$-$Zone Travel Time Skim Matrix

$\backslash$table$[[\backslash$table$[[$TAZ$-$TAZ travel$],[$time $($min$)]],1,2,3,4,5$