The Ritz-Carlton hotel in St. Louis has 140 standard rooms. It offers a $110 discount fare targeting leisure travelers and regular fare $200 targeting business travelers. Demand for low fare rooms arrives early and is abundant. The demand for high fare rooms follows a normal distribution with mean 40 and standard deviation 10. a) What is the optimal booking limit for the low-fare customers? b) Assume demand for regular-fare rooms is price insensitive (demand stays the same regardless of the regular fare). What value of the regular fare would make a booking limit of 70 optimal.