Problem $2.$ A study area has three TAZs, with travel time $($t$)$ in minutes in Table $1.$ Hand calculate the first two iterations of the doubly constrained gravity model. Use exp$(-t)$ as the friction factor. Productions and attractions for AM peak work trips are shown in Table $2.$

$1$

$2$

$3$

Figure $1.$ Three TAZs and their locations.

Table $1.$ Travel Times in Minutes between Zones

$\backslash$table$[[,1,2,3],[1,5,10,15],[2,20,10,8],[3,15,10,5]]$

Table $2.$ Productions and Attractions for Morning Peak$-$hour Work Trips

$\backslash$table$[[,$P$,$A$],[1,12,000,15,000],[2,35,000,23,000],[3,20,000,29,000]]$