Question

**Problem 16-09 (Algorithmic)**

The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities:

To |
||

From |
Special B |
MDA |

Special B |
0.90 | 0.10 |

MDA |
0.15 | 0.85 |

- Which brand appears to have the most loyal customers?

Special B

Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

- What are the projected market shares for the two brands? If
required, round your answer to three decimal places.

pie1 =

pie 2 =

Answer #1

A) We can see here that P(special B --> Special B) = 0.9
while

P( MDA --> MDA) = 0.85

As P(special B --> Special B) > P( MDA --> MDA)

**Therefore Special B customers are more loyal customers
here.**

b) Let the long term market shares for the two brands Special B
and MDA here be X and Y respectively. Then, we have here:

X + Y = 1

From first column, we have here:

X = 0.9X + 0.15Y

0.1X = 0.15Y

X = 1.5Y

Therefore, 2.5Y = 1

Y = 0.4

X = 0.6

**Therefore the projected market shares here are given
as:**

Problem 16-09 (Algorithmic)
The purchase patterns for two brands of toothpaste can be
expressed as a Markov process with the following transition
probabilities:
To
From
Special B
MDA
Special B
0.95
0.05
MDA
0.25
0.75
Which brand appears to have the most loyal customers?
Explain.
The input in the box below will not be graded, but may be reviewed
and considered by your instructor.
What are the projected market shares for the two brands? If
required, round your answer...

The purchase patterns for two brands of toothpaste can be
expressed as a Markov process with the following transition
probabilities:
To
From
Special B
MDA
Special B
0.80
0.20
MDA
0.25
0.75
Which brand appears to have the most loyal customers? (MDA or
special B)
Explain.
What are the projected market shares for the two brands? If
required, round your answer to three decimal places. π1 =_ , π2
=_

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 17 minutes ago

asked 38 minutes ago

asked 39 minutes ago

asked 40 minutes ago

asked 41 minutes ago

asked 41 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago