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MSBA7003 Quantitative Analysis Methods
Assignment 4 (Due October 29 at 9 a.m.; Please submit your solutions with the template)
Q1.
American Copiers sells and services copy machines to customers in 11 cities throughout the
United States. The company wants to set up service centers in three of these cities. After
American Copiers chooses the location of the service centers, it must assign customers in
each city to one of the service centers. For example, if it decides to locate a service center in
New York and then assigns its Boston customers to the New York service center, a service
representative from New York will travel to Boston when services are required there. The
distances (in miles) between the cities are listed in Table 1. The estimated annual numbers
of trips to the various customers are listed in Table 2. The goal of American Copiers is to
minimize the total annual distance traveled by its service representatives.
Table 1: Distance between Different Cities
Boston Chicago Dallas Denver
Los
Angeles Miami
New
York Phoenix Pittsburg
San
Francisco Seattle
Boston 0 983 1815 1991 3036 1539 213 2664 792 2385 2612
Chicago 983 0 1205 1050 2112 1390 840 1729 457 2212 2052
Dallas 1815 1205 0 801 1425 1332 1604 1027 1237 1765 2404
Denver 1991 1050 801 0 1174 2041 1780 836 1411 1765 1373
Los
Angeles
3036 2112 1425 1174 0 2757 2825 398 2456 403 1909
Miami 1539 1390 1332 2041 2757 0 1258 2359 1250 3097 3389
New
York
213 840 1604 1780 2825 1258 0 2442 386 3036 2900
Phoenix 2664 1729 1027 836 398 2359 2442 0 2073 800 1482
Pittsburg 792 457 1237 1411 2456 1250 386 2073 0 2653 2517
San
Francisco
2385 2212 1765 1765 403 3097 3036 800 2653 0 817
Seattle 2612 2052 2404 1373 1909 3389 2900 1482 2517 817 0
Table 2: Estimated Numbers of Annual Trips to Customers
Boston Chicago Dallas Denver
Los
Angeles Miami
New
York Phoenix Pittsburg
San
Francisco Seattle
885 760 1124 708 1224 1152 1560 1222 856 1443 612
Please develop a Python model with the PuLP or DoCplex package to find out which of the
following statement(s) is(are) true.
A) In the optimal solution, Dallas, San Francisco, and Boston should have service centers.
B) In the optimal solution, Dallas, San Francisco, and New York should have service centers.
C) In the optimal solution, Denver customers should be assigned to the service center in
Dallas.
D) In the optimal solution, Phoenix customers should be assigned to the service center in
Dallas.
E) None of the above.
Q2.
Jenny Wilson Realty is a real estate firm in Alabama. Jenny, the manager, wants to develop a
model to determine a suggested listing price based on the size, age, and the condition
(either good or excellent) of the house. A sample of historical data include selling price (Y),
the square footage (X1), the age (X2), and the condition (X3). Jenny runs a regression of Y
against X1, X2, and X3. Suppose Jenny would like to find out how much can renovating a
house and changing the condition from “good” to “excellent” affect the selling price. Which
of the following statement(s) is(are) true?
A) The estimated coefficient for X3 is not the true effect of interest.
B) Jenny should at least include the reputation of the property developer in the regression.
C) If the estimated coefficient for X3 is 250,000, it means that the renovating a house can
increase the selling price by \$250,000.
D) We can use the number of bathrooms should be included in the regression in order to
estimate how X3 influence Y.
E) None of the above.
Q3.
You are a factory manager and originally the workers are paid a fixed salary according to
their skill levels. You want to introduce a productivity-based salary in a hope to increase
worker productivity. To begin with, you randomly selected some male and female workers,
respectively, according to the numbers given in following table. The selected the workers
adopted the new salary scheme in the next month.
Gender Selected Not Selected Total Number
Male 15 35 50
Female 65 85 150
Their average productivities in the next month are shown in the following table.
Male 7 (selected) 6.0 (not selected)
Female 9 (selected) 7.5 (not selected)
Which of the following statement(s) is(are) true?
A) If you implement the new salary scheme for the whole factory, you can expect to
increase workers’ monthly productivity by 1.25 on average.
B) The naïve estimator of (7*15/80 + 9*65/80 – 6*35/120 – 7.5*85/120) is not biased.
C) Let D = 1 for selected workers and 0 otherwise. Let G = 1 for male workers and 0
otherwise. Suppose we run the regression model: Y = a + b*D + c*G + d*D*G + e, where
(a,b,c,d) are parameters and e is the error term. The estimated b should be about 1.5.
D) Among those not selected, their average productivity is expected to be increased by
1.375 if they also adopt the new policy.
E) None of the above.
Q4.
Consider the following causal graph.
Which of the following statement(s) is(are) true?
A) If we estimate the influence of X on Y through matching, we can condition on (B, D, W).
B) Using the regression model 𝑌 = 𝛼 + 𝛽𝑊 + 𝛾𝐴 + 𝜃𝐵 + 𝛿𝑋 + 𝜖, we can correctly estimate
the influence of X on Y given that the causal influences are all linear.
C) If the causal influences are all linear in this system, we can give a causal interpretation to
the estimated 𝛿 in this regression model: 𝑌 = 𝛼 + 𝛽𝐶 + 𝛿𝑋 + 𝜖.
D) If we condition on C, then D and Y are independent.
E) None of the above.
Q5.
You are running an online shopping website that focuses on fashion apparel. Your company
normally purchases a product from a supplier before the selling season starts. During the
season, customers that purchase the product can give a rating of the product on the website.
When the selling season ends, any leftovers will be shipped back to the supplier and partial
refund will be provided. You want to use the historical data to estimate how customer
rating of a product influences the sales of the product. You have prepared data for the
following variables:
Y: the total sales of a product
X: the average customer rating
P: the price of a product
S: the set of dummies that indicate the category of a product (e.g., male versus
female, season, and type)
W: the beginning inventory level
Which of the following statement(s) is(are) true?
A) Given the dataset, you can correctly estimate the influence of X on Y.
B) We can use P as an instrumental variable to estimate the influence of X on Y.
C) We can use S as an instrumental variable to estimate the influence of X on Y.
D) We can use W as an instrumental variable to estimate the influence of X on Y.
E) None of the above.

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