Given the following inputs to the gravity model, conduct trip balancing till the error bound converges to within $1\%.$ Then provide the aj$\_$out, aj$\_$adj, and MAPE $($Mean absolute percentage error$)$ at each iteration.

Table $2\mathrm{.}1$ Calibration $($Ground Truth$)$ OD Matrix

To Zone

From Zone $123$ Production$($pi$)$

$55015050250$

$6100300100500$

Attraction $($aj$)150450150$

Table $2\mathrm{.}2$ Friction Factor Table

Travel time $($min$)3456$

Friction Factor f$($dij$)0\mathrm{.}50\mathrm{.}40\mathrm{.}20\mathrm{.}1$

Table $3.$ Impedance Table

To Zone

From Zone $123$

$5635$

$6345$