Given the following utility function for the work trip U = a -0.003C, -0.047, 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. a) Calculate the market shares of the following travel modes in a corridor: Mode i Automobile Express bus Regular bus Bike aj 0.47 0.24 0.00 0.11 Ci (cents) 130 60 30 0.00 Ti (minutes) 30 45 55 70 b) Estimate the effect that a proposed 30% increase 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.