$[30$ pts$]$ Region A can be divided into $3$ sections A$,$ B$,$ and C$.$ Costs of inter$-$sectional travel is shown

below, while intra$-$sectional travel within sections $A,B,$ and $C$ are known to be $3,1,$ and $2$ minutes,

respectively. With total trip ends given in the following table, estimate the OD trip matrix using a gravity

model of type: $T_{ij}=a_l{b}_j{c}_{jj}^a{e}^{-c_{lj}}$ where a and $$ have values of $0\mathrm{.}5$ and $0\mathrm{.}1,$ respectively.