THE INTERNATIONAL UNIVERSITY (IU)
School of Business
Course: Quantitative Methods for Business
INDEX 1
MIDTERM EXAMINATION
QUANTITATIVE METHODS FOR BUSINESS
Dean of School of Business
Lecturer:
Student ID:
Duration:
minutes
150
Date:
Nov 9th , 2014
Name:
Dr. Nguyen Van Phuong
Mr. Nguyen Bac Huy
INSTRUCTIONS:
1.
This is an open book examination. No laptops, PDA.
2.
Use of calculator is allowed; discussion and material transfer are strictly prohibited.
3.
Answer the multiple-choice questions in your question sheet. The question sheet must be submitted.
Total pages: 04 (including this page)
PART I: MULTIPLE CHOICE: (30 points)
Given the following two-person game, use the payoff table for 3 following questions:
Player B
Player A
A1
A2
B1
-6
7
1.
A.
B.
C.
D.
The probability that player A choose strategy A2 is:
6/11
5/11
9/22
13/22
2.
A.
B.
C.
D.
The expected value of the game is:
1/11
10/11
-10/11
-1/11
B2
4
-5
3. Which player would you like to be?
A. Player A
B. Player B
Midterm Exam – Quantitative Methods for Business
Index 1
1
THE INTERNATIONAL UNIVERSITY (IU)
School of Business
4.
A.
B.
C.
D.
Course: Quantitative Methods for Business
Which following statement is WRONG about seasonal index?
Seasonal index is often used in multiplicative time series forecasting model
The range of seasonal index is: [0,1]
The sum of the indices should be the number of seasons
When no trend is present, if the seasonal index is 0.8, that mean the season tend to be below the
average
Using the following payoff table for 2 following questions:
alternatives
Large shop
Medium shop
Small shop
Saving money
Probability
Good market
1000
700
200
100
0.3
State of nature
stable market
600
400
100
100
0.4
Bad market
- 800
-300
-100
100
0.3
5. Using EMV, what is the best strategy?
A. Large shop
B. Medium shop
C. Small shop
D. Saving money
6.
A.
B.
C.
D.
The maximum of cost you are willing to pay for the perfect information is:
$ 610
$ 570
$ 300
$ 270
7.
A.
B.
C.
D.
What is NOT true about Expected Opportunity Loss?
EOL is the cost of not picking the best solution
Minimum EOL will always result in the same decision as maximum EMV
Minimum EOL will always equal EVPI
Maximum EOL will always equal EvwPI
8.
A.
B.
C.
D.
About exponential smoothing, which of the following is right?
It is the qualitative forecast method
It is a type of moving average
It is difficult to use
The lower α, the better forecasted result
Midterm Exam – Quantitative Methods for Business
Index 1
2
THE INTERNATIONAL UNIVERSITY (IU)
School of Business
Course: Quantitative Methods for Business
9. Using data in the following table, what is the value of forecasting include trend (FIT) of period
2?
A.
B.
C.
D.
period
demand
1
2
38
40
Unadjusted forecast
(α=0.3)
37
Trend (β=0.7)
0.4
37.3
37.63
36.97
37.4
10. A na𝑖̈𝑣𝑒 forecast for monthly sales is equivalent to:
A. A 3-month moving average model
B. An exponential smoothing model with α = 0
C. A seasonal model in which the seasonal index is 1
D. None of above
PART II: WRITING: (70 points)
Question 1: (5 points)
Consider the following two-person zero-sum game. Both players simultaneously call out one of the
numbers {2, 3}. Player 1 wins if the sum of the numbers called is odd and player 2 wins if their sum is
even. The loser pays the winner the product of the two numbers called (in dollars).
a) Develop the payoff table for this game?
b) What are the optimal strategies and the value of the game?
Question 2: (30 points)
The uses of a certain material (kilograms) are shown in following table:
Period Material used Period Material used Period Material used
Y1 / Q1
350
Y2 / Q1
157
Y3 / Q1
211
Y1 / Q2
145
Y2 / Q2
226
Y3 / Q2
85
Y1 / Q3
64
Y2 / Q3
126
Y3 / Q3
340
Y1 / Q4
253
Y2 / Q4
187
Y3 / Q4
236
a) Forecast the amount of material will be used for quarter 1 of next year (year 4) by using
Weighted Moving Average of 3 periods given that the weights are known as 3 for last month, 2
for two months ago & 1 for three months ago and Exponential smoothing with smoothing
constants of 0.7 (assuming Y1 / Q1 forecast of 300 kilograms. Which method is better? Why?
b) Determine the seasonal index for each quarter by using centered moving average (CMA)
approach.
Midterm Exam – Quantitative Methods for Business
Index 1
3
THE INTERNATIONAL UNIVERSITY (IU)
School of Business
Course: Quantitative Methods for Business
Question 3: (35 points)
The Dynamax Company is going to introduce one of two new products: a widget or a hummer. The
market conditions (favorable or unfavorable) and associated probabilities will determine the profit or
loss the company realizes, as shown in the following payoff table.
,
Product
Widget
Hummer
Market Conditions
Favorable
Unfavorable
0.68
0.32
$145,000
-$50,000
75,000
-10,000
The Dynamax currently considers paying $15,000 to a market research firm do a marketing test
for them. The test has only two possible results: positive or negative. Based on the historical
cases, the market research firm supplied more information to Dynamax as following:
 If the market is favorable, the result will be positive with the high probability of 0.85;
 In case the market is unfavorable, the result will be negative with the probability of 0.80.
The Dynamax wants to analyze this sequence of decisions: conducting the marketing test and
then selecting the appropriate product based on the test result.
i. Draw the decision trees for this problem.
ii. Select the best decisions for this company.
iii. Determine how much the Dynamax would be willing to pay to a market research firm to
gain better information about future market conditions.
GOOD LUCK!
Midterm Exam – Quantitative Methods for Business
Index 1
4