The H&R Block Office in Fairfax wants to make the most tax preparation profit on

Question

The H&R Block Office in Fairfax wants to make the most tax preparation profit on April 15. For this purpose, it allows clients to reserve 30 min blocks from 7 am until 5 pm. The clients who make reservations on April 10 or before are those who prepare in advance for tax filling. Moreover, they have several alternative companies other than H& R Block to file their tax. On the other hand, the clients who make reservations on April 11 and after do not have many alternatives. Thus, these clients can be charged more. Specifically, H & R Block determines to charge $75 for 30 min sessions if they are reserved before April 10, the same number is $218 for reservations after April 11. From the previous years, we know the distribution of the number of reservations made over April 11-15:

Number of Number of reservations over April 11-15

15 16 17 18 19 20 21 22 23 24 25

Probability 0.05 0.08 0.11 0.13 0.20 0.15 0.11 0.06 0.05 0.04 0.02

How many sessions should be protected for late reservers?

Explanation / Answer

Expected no of reservations over april 11-15:

product of no of reservations and probabilities

=15*0.05 + 16*0.08 + 17*0.11 + 18*0.13 + 19*0.20 + 20*0.15 + 21*0.11 + 22*0.05 + 23*0.05 + 24*0.04 + 25*0.02

= 19.28

no of sessions to be protected for late reservers = 20 blocks

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