An airport has a shuttle bus that connects the main terminal to a nearby rail station. The shuttle operates with a 15 minute headway between dispatches from the terminal. Suppose that the passengers arrive at the shuttle stop at a rate lambda = 120 passengers/hour. Suppose that the airport shuttle service costs the operating agency $50 per dispatch from the bus stop to cover labor, fuel, maintenance, etc. and that each passenger values their time while waiting for the shuttle at beta $/hour. (a) Write an expression for the total generalized cost per hour for operations and passenger waiting in terms of the variables given. (b) Assume that the value of time is beta = 20 $/hour, calculate the optimal frequency that minimizes the total generalized cost. (c) Calculate the minimum total generalized cost