Problem $1$: Estimation of a gravity model $[20]$

You are provided with the inter$-$zonal travel time matrix $($Table $1)$ and the inter$-$zonal trip interchange $($flow$)$ matrix $($Table $2)$ for the base year for a five$-$zone system. Calibrate a production$-$constrained gravity model. Use the following discrete time periods $($in minutes$)$ in calibration: $\{0-5\},\{5\mathrm{.}1-10\},\{10\mathrm{.}1-15\},$ and $\{15\mathrm{.}1-20\}.$ Perform two iterations.

Table $1.$ Base year inter$-$zonal travel time matrix

$\backslash$table$[[t_f,1,2,3,4,5$