BUS 314 Operations Research Assignment

Assignment Help Management Theories

Reference no: EM132491529

BUS 314 Operations Research Assignment, College of Management & Administration - William V.S. Tubman University, Liberia

Instruction - Review your lecture notes up to where we stopped (Markov Processes) and carefully answer/solve the following problems. Illustrate your solutions and or answers with diagrams wherever applicable.

Question 1 - Management of the New Fangled Softdrink Company believes that the probability of a customer purchasing Red Pop or the company's major completion, Super Cola, is based on the customer's most recent purchase. Suppose the following transition probabilities are appropriate:

From	To
From	Red Pop	Super Cola
Red Pop	0.9	0.1
Super Cola	0.1	0.9

a. Show the two-period tree diagram for a customer who last purchased Red Pop. What is the probability that this customer purchases Red Pop on the second purchase?

b. What is the long-run market share for each of these two products?

c. A Red Pop advertising campaign is being planned to increase the probability of attracting Super Cola customers. Management believes that the new campaign will increase the probability of a customer switching from Super Cola to Red Pop is 0.15. What is the projected effect of the advertising campaign on the market shares?

Question 2 - The computer software system during registration at William V.S. Tubman University has been experiencing computer downtime. Let us assume that the trials of an associated Markov Process are defined as 1-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities:

From	To
From	Running	Down
Running	0.90	0.10
Down	0.30	0.70

a. If the system is initially running, what is the probability of being down in the next hour operation?

b. What are the steady-state probabilities of the system in the running state and in the down state?

Question 3 - One cause of the downtime in Problem 2 was traced to a specific piece of computer hardware. Management believes that switching to a different hardware component will result in the following transition probabilities:

From	To
From	Running	Down
Running	0.95	0.05
Down	0.60	0.40

a. What are the steady-state probabilities of the system in the running and down states?

b. If the cost of the system being down for any period is estimated to be $500 (including lost revenues for time down and maintenance), what is the breakeven cost for the new hardware component on a time-period basis?

Question 4 - Data collected from selected major metropolitan areas in Montserrado County in Liberia show that 2% of individual living the city limits move to the suburbs during a 1-year period while 1% of individuals living in the suburbs move to the city during a 1-year period. Answer the following questions assuming this process is modeled by a Markov process with two states: city and suburbs.

a. Show the matrix of transition probabilities.

b. Compute the steady-state probabilities.

c. In a particular metropolitan area, 40% of the population live in the city and 60% of the population live in the suburbs. What population changes do your steady-state probabilities project for this metropolitan area?

Question 5 - The purchase patterns of two brands of toothpaste can be expressed as a Markov Process with the following transition probabilities:

From	To
From	Special B	MDA
Special B	0.90	0.10
MDA	0.05	0.95

a. Which brand appears to have the most loyal customers? Explain.

b. What are the projected market shares for the two brands?

Question 6 - Suppose that in Problem 8 a new toothpaste brand enters the market such that the following transition probabilities exist:

From	To
From	Special B	MDA	T-White
Special B	0.80	0.10	0.10
MDA	0.05	0.75	0.20
T-White	0.40	0.30	0.30

a. What are the new long-run market shares? Which brand will suffer most from the introduction of the new brand of toothpaste?

Reference no: EM132491529

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