Given the following utility function for the work tripU, $=$ a$,-0\mathrm{.}003$C$,-0\mathrm{.}047$;Where U$,$ is the utility for mode i$,$ a$,$ is the modal constant term for mode i$.$ C$,$ is the travel cost in cents for mode i$,$ and T$,$ is the travel time in minutes by mode i$\mathrm{.}8)$ Calculate the market shares of the following travel modes in a corridor:b$)$Estimate the effect that a proposed $30\%$ inerease in the cost associated with the automobile will have on mode split in the corridor. You should show all steps to your solution of the problem.