Discuss the below:
The manager of the 420-room SleepyTime Hotel is trying to decide how many rooms to reserve for vacationers who book less than two weeks in advance. Demand for the "early booking" rooms is unlimited at the price of $240/day. Demand for the "late booking" rooms averages around 120 rooms/day, and varies by about 15 rooms/day. The rate for 'late booking' rooms is $320/day.
Q: How many rooms should be held for "late booking" and "early booking?"
Assuming there will be no change in demand caused by changes in price, what price would need to be charged for "late booking" rooms in order to justify holding 120 rooms for "late bookers?"