Answer:
a. The number of reservations should the manager accept is 225 bookings
b. The probability that the manager will have to compensate for customers when there are not enough seats is 0.2317
Step-by-step explanation:
According to the given data we have the following:
Cost of Overage Co = 800
Cost of Underage Cu = 475
Hence, Critical Ratio = Cu/(Cu+Co)
Critical Ratio = 475/1275
Critical Ratio = 0.3725
To calculate the number of reservations should the manager accept we would have to calculate first the Optimal Number of Overbooking as follows:
Z = NORM.S.INV(0.3725) = -0.3251
Optimal Number of Overbooking = Mean of No show + Z*Sd of No show
Optimal Number of Overbooking = 30 - 0.3251*15
Optimal Number of Overbooking = 25.12
Optimal Number of Overbooking = 25
a. Therefore, Number of reservation = Capacity + Overbooking = 200+25 = 225 bookings
b. Number of Overbooking = 220 - 200 = 20
Manager will have to compensate if there will be less than or equal to 19 No show.
Therefore, to calculate the probability that the manager will have to compensate for customers when there are not enough seats we have to calculate the following formula:
P(Compensation) = P(No Show <= 19) = P(Z <= (19-30/15))
P(Compensation) = P(Z<= - 0.7333)
P(Z< - 0.7333) = NORM.S.DIST(-0.7333,1)
P(Z< - 0.7333) = 0.2317
P(compensation) = 0.2317
Probability of Compensation = 0.2317
