Given the following information, and using the generalized capacity restraint link performance function $($BPR method$),$ estimate the flow that will use the three routes using user equilibrium assignment. A flow of $8,800$ vehicles in the peak hour is to be distributed between the three routes whose properties are given in the following table.

$\backslash$table$[[$Link Performance,Route $1,$Route $2,$Route $3],[$Free$-$flow travel time $($min$.),17\mathrm{.}0,15\mathrm{.}5,12\mathrm{.}5],[$Capacity $($veh$/$h$),3800,4200,6600],[,0\mathrm{.}3,0\mathrm{.}5,0\mathrm{.}6],[,2\mathrm{.}5,3\mathrm{.}5,4\mathrm{.}5]]$

There are three alternative routes connecting node X and Y $.$ The drivers are free to choose routes $1,2,$ or $3$ when leaving from node $x.$ The total number of trips between $x$ and $Y$ is $7500$ trips.