The Harriet Hotel in downtown Boston has 100 rooms that rent for $150 per night. It costs the hotel $30 per room in variable costs (cleaning, bathroom items, etc.) each night a room is occupied. For each reservation accepted, there is a 5% chance that the guest will not arrive. If the hotel overbooks, it costs $200 to compensate guests whose reservations cannot be honored. How many reservations should the hotel accept if it wants to maximize the average daily profit?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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The Harriet Hotel in downtown Boston has 100 rooms that rent for $150 per night. It costs the hotel $30 per room in variable costs (cleaning, bathroom items, etc.) each night a room is occupied. For each reservation accepted, there is a 5% chance that the guest will not arrive. If the hotel overbooks, it costs $200 to compensate guests whose reservations cannot be honored. How many reservations should the hotel accept if it wants to maximize the average daily profit?

Wk_8_Asg--Template XLSX
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Default (Ca.
B I S A
100%
.00 123-
11
- fx |
A1
A
B
F
G
H
J
K
L
M
1
Harriet Hotel, Boston
3
Rooms Available
100
Data
Probability (No Show)
4
0.05
Data
Reservations
Decision: Vary between
to 115 using the Dec
Table in Crystal Ball
Guests Arriving
Assumption: Use binomial with P(Head) = 1- P(No Show) and number of tosses = Reservations
6
108
7
Data
$150
$30
$200
Revenue
$16,500
Enter formula
Variable Costs
Enter formula
$3,000
$1,600
$11,900
10
Overbooking Costs
Enter formula
11
Profit
Forecast: Enter formula
12
13
Transcribed Image Text:Wk_8_Asg--Template XLSX File Edit View Insert Format Data Tools Help Last edit was seconds ago Default (Ca. B I S A 100% .00 123- 11 - fx | A1 A B F G H J K L M 1 Harriet Hotel, Boston 3 Rooms Available 100 Data Probability (No Show) 4 0.05 Data Reservations Decision: Vary between to 115 using the Dec Table in Crystal Ball Guests Arriving Assumption: Use binomial with P(Head) = 1- P(No Show) and number of tosses = Reservations 6 108 7 Data $150 $30 $200 Revenue $16,500 Enter formula Variable Costs Enter formula $3,000 $1,600 $11,900 10 Overbooking Costs Enter formula 11 Profit Forecast: Enter formula 12 13
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