Managers at the Dew Drop Inn are concerned about the increasing number of guests
ID: 429168 • Letter: M
Question
Managers at the Dew Drop Inn are concerned about the increasing number of guests who make reservations but fail to show up. They have decided to institute a policy of overbooking like larger hotel chains. The prot from a paying guest averages $50 per room per night. The cost of putting up a guest at another hotel is $100 per room per night. Records show the following number of no-shows over the past three months:
No-Shows Frequency 0 18 1 36 2 27 3 9
How many rooms should Dew Drop overbook?
Please show work so I can better understand how to solve.
Explanation / Answer
The data about No-Shows and number of guests( booked but not able to provide accomodation) at another hotel is mixed up. Let me try to assume the following; x represents number of no-shows and f represents the frequency, then x=0, f=18 is one observation x=1, f=36 second, x=2, f=27 third and x=3, f=9 fourth and last
Now expected number of No-Shows is = Sum of products of variable values with corresponding frequecies divided by sum of frequencies = sum of x*f / sum of f
Expected number is also called Average (mean) = (0*18 + 1*36 + 2*27 +3*9} / ( 18+36+27+9} = 1.3
Therefore we can assume that there are 1.3 no-shows on the average for the day.
The average cost of No-Shows (loss of profit) = 1.3*50 =$65 per room per night whereas putting up a guest at another hotel is $100 per room per night, even with rounding two 2 No-Shows, both are equal to $100 & $200 so policy needs estimate for number of guests to be put up at another hotel in case of overbookings.
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