Booking/Overbooking. Critical fractiles

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.

How many rooms should be held for "late booking" AND "early booking?"

....and 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 justify holding 120 rooms for "late bookers?"

I think this is a critcal fractile problem?


I am supposed to use one or more of the following techniques (and we are instructed to always use 95% confidence level, unless the problem states otherwise):

-Confidence intervals and hypothesis testing
-Decision trees (and their use in solving managerial problems),
-Critical fractile analysis (and its use in determining optimal demand levels),
-Analysis of variance/ANOVA (and its use in understanding differences between group means),
-Chi-square (cross tabs/contingency table) analysis (and its use in determining differences between group proportions),
-Regression, single and multiple (and its use in understanding relationships between dependent and independent (explanatory) variables), and
-Optimization modeling (and its use in determining the best solution given a set of constraint).

I do not know how to do this.  Help!!