Inn at Penn has 250 rooms. For regular-fare customers, rooms are priced at $300 per night while the rooms are priced at $700 per night for the high-paying customers who generally arrive at the last minute. The demand for such high fare customers is distributed normally with mean 70 and std.dev. 22. Assume that there is ample demand for regular-fare customers, but rooms cannot be sold to these customers at the last minute (end of a day).
What should the protection level for the high fare customer be to maximize expected profit? Note: The protection level is the number of rooms not sold to regular customers and kept aside for sale to high fare customers. If you over-protect (i.e., the protection level is too high), and there are fewer high fare customers than the protection level, you lose the regular fare revenue opportunity; if you under-protect and there are more high fare customers than the protection levels, you lose the additional revenue from the high fare customers.
Please show formulas,
a. Less than 50
b. At least 50 but less than 60
c. At least 60 but less than 65
d. At least 65 but less than 70
e. At least 70 but less than 75
f. At least 75 but less than 80
g. At least 80