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Content of the Final Examination

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Reading Material and References

D.R.Anderson, D.J.Sweeney, T.A.Williams. Quantitative Methods for Business, South-Western College Publishing, 11-th edition.

L-drive (Lectures and Tutorials).

Content of the Final Examination

  1. Decision Analysis(/1/ Chapter 4, /2/ Lecture 2, Case Set 2)
  2. Utility(/1/ Chapter 5, /2/ Lecture 3, Case Set 3)
  3. Game Theory(/1/ Chapter 5, /2/ Lecture 4, Case Set 4)
  4. Forecasting(/1/ Chapter 6, /2/ Lecture 5, Case Set 5)
  5. Linear programming(/1/ Chapter 7, /2/ Lecture 6’, Case Set 6’)
  6. Markov Processes(/1/ Chapter 16, /2/ Lecture 11, Case Set 11)
  7. Leontief Input-Output Analysis(/2/ Lecture 10, Case Set10)
  8. Inventory Models(/1/ Chapter 13, /2/ Lecture 7, Case Set 7)

 

Problem 1. Decision Analysis. Utility

A firm has three investment alternatives. Payoffs are in thousands of dollars.

 

  Economic Conditions
Decision Alternative Up s1 Stable s2 Down s3
Investment A, d1      
Investment B, d2      
Investment C, d3      

 

a. Using the opportunity regret approach, which decision is preferred?

b. Assume that the following utilities are assigned. Do the utilities re­flect the behavior of a risk taker or a risk avoider?

 

Profit Utility
$1,500,000 0.80
$1,000,000 0.60
$500,000 0.30

 

c. Use expected utility to make a recommended decision.

The joint probabilities associated with investment alternatives and economic conditions are as follows:

 

  Economic Conditions
Decision Alternative Up s1 Stable s2 Down s3
Investment A, d1 0.4 0.5 0.1
Investment B, d2 0.2 0.3 0.5
Investment C, d3 0.5 0.3 0.2

 

Problem 2. Game Theory

 

Company A and Company B, are competing for a given consumer market. Each company is considering four advertising options. Depending on the options used by each company, a certain percentage of consumers will switch from one company to the other. After performing market studies, it was determined that the entries in the payoff table (below) represent the percentage of Company B customers that will switch to Company A.

Company B

  b1 b2 b3 b4
a1 7.25 0.15 14.76 17.17
a2     15.87 18.3
a3 7.92 -9.17 10.7 14.1
a4 -6   -5.4 -5.17

 

Company A

a. Does the game have a saddle point and a pure strategy?

b.Reduce the game to 2x2 game.

c. Determine the optimal mixed strategy solution.

d. What is the value of the game?

 

Problem 3. Forecasting (with trend)

The data in the table are typical prices for a barrel of crude oil for the indicated years:

 

Year Crude oil($per barrel)
  111.4
  111.3
  110.7
  111.8
  110.5
  109.8
  109.0
  108.2
  105.5
  106.4
   

 

a. Graph this time series. Does a linear trend appear?

b. Develop a linear trend equation for this time series.

c. Draw graph of the trend. Use the trend equation to estimate the price for a barrel of crude oil for 2016.

 

Problem 4. Linear programming

 

A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I and Machine II per month are 180 and 300. The time requirements and profit per unit for each product are listed below.

 

  A B C
Machine I      
Machine II      
Profit      

 

a. Develop the linear programming model of the problem

b. Show the feasible region

c. How many units of each product should be manufactured to maximize profit, and what is the maximum profit

 

Problem 5. Markov Processes

 

Company I, Company II, Company III, and Company IV compete against each other, and the transition matrix for people switching from company to company each year is given below.

 

      To    
    I II III IV
  I 0.5 0.1 0.1 0.3
From II 0.4 0.3 0.1 0.2
  III 0.2 0.2 0.2 0.4
  IV 0.1 0.4 0.3 0.2

 

 

Find the following.

 

a) If the initial market share is 10% for Company I, 20% for Company II, 40% for Company III, and 30% for Company IV what will the market share be next year?

b) If this trend continues, what is the long range expectation for the market? (Use Cramer’s Rule)

 

Problem 6. Leontief Input-Output Analysis

 

Assume that an economy is based on three industrial sectors, agriculture, building and energy. Production of dollar’s worth of agriculture requires an input of $0.3 from agriculture sector, $0.1 from the building sector, and $0.2 from the energy sector. Production of dollar’s worth of building requires an input of $0.2 from agriculture sector, $0.1 from the building sector, and $0.1 from the energy sector. Production of dollar’s worth of energy requires an input of $0.2 from agriculture sector, $0.1 from the building sector, and $0.1 from the energy sector.

a. Find the technology matrix T

b. Find (I – T) -1

c. Find the output from each sector that is needed to satisfy a final demand of $5 billion for agriculture, $ 10 billion for building, and $ 15 billion for energy.

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