An electronic version of solutions

• An electronic version of solutions should be uploaded to Learn@PolyU.
• You should type your answers in a pdf/word file.
• The file name should start with your name, e.g., “Leung Wing Yi.pdf” or “Leung Wing
Yi-Quiz 1.pdf”.
• Due time: noon 20 Feb (Sun)
• You can use calculators, but you must show your calculations.
• The values of “X” in Question 1, “Y” in Question 3 and “Z” in Question 4 are shown in
the table below. Different students may have different values of “X”, “Y” and “Z”. You
should use the values that are in the same row as your Student ID in the table.
Student No. “X” in Q1 “Y” in Q3 "Z" in Q4
21061559G 0.05 28 0.1
21064101G 0.1 28 0.1
21006161G 0.05 32 0.25
21105833G 0.05 32 0.25
21063889G 0.05 32 0.1
21066829G 0.1 32 0.1
21108771G 0.1 28 0.25
21106229G 0.1 32 0.25
21058465G 0.1 32 0.25
21105978G 0.05 32 0.1
21050996G 0.05 32 0.1
21066477G 0.05 28 0.1
21001296G 0.1 28 0.25
21068464G 0.1 32 0.25
21036312G 0.05 32 0.1
21069737G 0.05 32 0.1
21064246G 0.1 28 0.25
21053646G 0.1 32 0.25
21060454G 0.1 32 0.25
21109273G 0.05 32 0.1
21060385G 0.05 28 0.1
21052373G 0.05 28 0.1
21057415G 0.1 32 0.25
21026748G 0.05 28 0.1
21063219G 0.05 32 0.25
21053492G 0.1 32 0.1
21026702G 0.05 32 0.1
21060461G 0.05 28 0.25
21052023G 0.05 28 0.25
21026587G 0.05 32 0.25
21055748G 0.1 32 0.25
21068487G 0.05 28 0.1
21045091G 0.1 32 0.1
Question 1 (2 points)
(Replace “X” in the question with its value in the table in the guideline.) Royal Plaza Hotel has
200 rooms with standard queen-size beds and two rates: a full price of HK$600 for business
travelers and a discount price of HK$375 for leisure travelers. To receive the discount price, a
customer must purchase the room at least two weeks in advance (this helps to distinguish
between leisure travelers, who tend to book early, and business travelers, who value the
flexibility of booking late). For a particular Thursday night, the hotel estimates that the demand
from leisure travelers could fill the whole hotel while the demand from business travelers is
distributed as follows.
Number of business travelers Frequency
28 0.1
30 0.1
33 0.05
35 0.05
37 X
38 0.2-X
40 0.15
42 0.1
44 0.1
47 0.05
50 0.05
53 0.05
Q1.1: Find the optimal protection level for full-price rooms (the number of rooms to be
protected from sale at a discount price). (0.5 point)
Q1.2: The competitor of Royal Plaza Hotel, Kimberley Hotel, declared a fare war by slashing
business travelers’ prices down to HK$500. Royal Plaza Hotel had to match that fare to keep
demand at the same level. Does the optimal protection level increase, decrease, or remain the
same? Explain your answer. (1 point)
Q1.3: What number of rooms (on average) remain unfilled if we establish a protection level of
39 for the full-priced rooms? (0.5 point)
Question 2 (1.5 points)
A manufacturer of cloth is considering the addition of a new plant to absorb the backlog of
demand that now exists. The primary location being considered will have fixed costs of $8,000
per month and variable costs of 60 cents per unit produced. Each item is sold to retailers at a
price that averages 80 cents.
Q2.1 What volume per month is required in order to break even? (0.5 point)
Q2.2 What profit would be realized on a monthly volume of 60,000 units? (0.5 point)
Q2.3 What volume is needed to obtain a profit of $16,000 per month? (0.5 point)
Question 3 (2 points)
(Replace “Y” in the question with its value in the table in the guideline.) There are six container
terminals, and the parameters to measure the performance of these terminals are listed in the
following table.
Terminal Quay Length (1000 m) Throughput (Million
TEU)
Revenue (100 Million Dollars)
T1 4 8 16
T2 8 12 12
T3 4 16 8
T4 12 18 Y
T5 10 20 30
T6 24 12 24
Use data envelopment analysis (DEA) to compare the performances of these six terminals using
a single input (Quay Length) and two outputs (Throughput and Revenue) by calculating the
relative efficiency of each terminal. (2 points)
Question 4 (2 points)
(Replace “Z” in the question with its value in the table in the guideline.) A direct-sale store of
Teavana plans to offer a gift basket of oolong teas for the holiday season. They plan on placing
one order and any leftover inventory will be discounted at the end of the season. The gift basket
sells $50 each, the unit purchase cost is $32, and leftover baskets will be sold $23 each. The
best estimate for demand is:
Quantity (Q) Relative frequency
1 0.15
2 0.1
3 0.1
4 0.05
5 0.15
6 Z
7 0.4-Z
8 0.05
Q4.1 If they purchase only 3 baskets, what is the probability that some demand will not be
satisfied? (0.5 point)
Q4.2 How many baskets should the store purchase to maximize its expected profit? (0.5 point)
Q4.3 Suppose they purchase 7 baskets. How many baskets should they expect to have to mark
down at the end of the season? (0.5 point)
Q4.4 Suppose the store orders 8 baskets. What is its expected profit? (0.5 point)