1. How many passengers should this airline overbook?
|
Passengers Overbooked |
||||||
|
No Shows |
P(NS) |
0 |
1 |
2 |
3 |
4 |
|
0 |
.30 |
180* |
130 |
80 |
30 |
– 20 |
|
1 |
.25 |
100 |
180 |
130 |
80 |
30 |
|
2 |
.20 |
20 |
100 |
180 |
130 |
80 |
|
3 |
.15 |
– 60 |
20 |
100 |
180 |
130 |
|
4 |
.10 |
–140 |
– 60 |
20 |
100 |
180 |
|
Expected Profit: |
$ 60 |
$101 |
$109.50 |
$ 92 |
$ 55 |
a. overbook by 0
b. overbook by 1
c. overbook by 2
d. overbook by 3
e. overbook by 4
2. A front desk receptionist at the Hilton Back Bay answers 3 types of calls and the mix of reservation and time to process each type are fairly predictable:
Reservation type 1: 60% 5 minutes
Reservation type 2: 30% 3 minutes
Reservation type 3: 10% 21 minutes
If he works 6 hours a day, five days a week:
a. What is his weekly capacity in calls? ________ calls
b. If he answers 200 calls per week on average, what is his capacity utilization? __________%
3. The airflow of three floors at the Hotel and 24 meeting/event rooms is performed by fans that take in outside air, filter it, and cool or heat it to 65 degrees Fahrenheit. To monitor performance, air temperature is measured in four locations each day by the hotel staff. The standard deviation for the temperature has been 3 degrees.
If temperature is supposed to stay within 65 degrees ±4 degrees, is the process capable? Assume average temperature has been 65 degrees.
o No o Yes
Briefly explain:
- 4. The Company manufactures parts for the type of boots worn by students using two computerized numerically controlled injection molding machines. The company wants to decide which machines are capable of producing the specific part for the waterproof rubber toe including design specifications of 1 inch ± 0.06 inch. The machines have the following process parameters:
Machine 1: ?= 1, ? = 0.01
Machine 2: ?= 1, ? = 0.03
Is either of the machines capable of doing the job?
5. A parasailing boat operating out of a resort has recorded the no-show experience due to sharks in the area shown below over the past 20 boat excursions. To avoid the opportunity of losing the $50 fee charged per parasailer, the boat captain is considering a policy of accepting more reservations than his boat has capacity. When this policy results in turning away disappointed parasailers, he plans to hire his brother to accommodate the overbooked parasailers at $120 each.
No-show 0 1 2 3 4
- Frequency 4 5 6 3 2
- Using the “critical fractile” probability, P(d < x), how many reservations would you recommend overbooking?
- What is the expected loss per parasail boat excursion, if only two reservations are overbooked?
