In response to the government requirement to publish on-time statistics, the airlines have been trying to improve their performance for arrival times. Although there is always room for improvement, a great deal of the uncertainty in the duration of airline flights is due to weather conditions and congestion not under the direct control of the airline. One way to deal with the problem given the government regulations is simply to increase the published length of the flight. With more slack in the schedule, more planes arrive early or on-time. This question addresses the amount of slack that should be put in the schedule.

Suppose for a particular Rochester-Newark flight the airline has determined that the gate-to-gate time has a normal distribution with mean 65 minutes and standard deviation of 5 minutes. The difficulty with making the scheduled time too large is that the airline must pay the pilot and crew for the gate-to-gate scheduled time not the actual time. This cost is $210/hour.

a) If the airline wants an on-time performance of 90% on-time flights, how much time should they schedule for this Rochester-Newark flight? Round your answer up to the nearest minute. (Show your calculation)

b) What is not stated in this problem is the rate in $/hr that the airline incurs if a flight is late, in terms of future lost sales because a passenger is annoyed with the late flight arrival, and perhaps he/she missed a meeting or the connection for another flight. Yet, for the on-time performance percentage that the airline picked in the last part of the problem there is a cost rate that would make that performance percentage optimal. What is this implied cost rate for a late flight in dollars/hour for this level of performance? (show your calculation)