$($d$)$ In a three$-$zone area, the trips generated $($in thousands$)$ at the zones are

respectively $5,5$ and $45,$ and the trips attracted $($in thousands$)$ to the

zones respectively are $20,30$ and $5.$ The deterrence function $f(c_j)$ has

the following form:

$f(c_{ij})=t_{ij}^{-1}$

where $t$ is the travel time for each zone pair as shown in Table Q$1($d$).$

What would be the estimated values of the deterrence function?

$($e$)$ Use the expression of the gravity model below to estimate the trip

distribution matrix for this area. Assume $K_{ij}=1$ for all $i,j.$

$T_{ij}=A_i{O}_i{B}_j{D}_{j}f(c_{ij})K_j$