Relating two vectors using matrix multiplication:

Suppose that at the beginning of each year, people change the beer they drink.

Let for $i=1,2,3,....xi$ be the number of people who prefer beer “i” at the beginning of this month, and $yi$ be the number of people who prefer beer “i” at the beginning of next month.

Since 30% of the people who prefer beer 1 switch to beer 2 and 20% of the people switch to beer 3, so the remaining 50% continue to be with beer 1. Also, 10% of people who prefer beer 3 switch to beer 1.

Hence, the number of people who prefer beer 1 in the beginning of next month is given below:

$y1=0.5x1+0.1x3$

Now, 30% of the people who prefer beer 2 switch to beer 3 and the remaining 70% of the people continue to be with beer 2. Also, 30% of people who prefer beer 3 switch to beer 2 and 30% of the people who prefer beer 1 switch to beer 2.

Hence, the number of people who prefer beer 2 in the beginning of next month is given below:

$y2=0.3x1+0.7x2+0.3x3$

Then, 30% of the people who prefer beer 3 switch to beer 2 and 10% of the people switch to beer 1, so the remaining 60% continue to be with beer 3. Also, 20% of people who prefer beer 1 switch to beer 3 and 30% of the people who prefer beer 2 switch to beer 3.

Hence, the number of people who prefer beer 3 in the beginning of next month is given below:

$y3=0.2x1+0$

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Chapter 2.1, Problem 1P

Chapter 2.1, Problem 3P

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Chapter 2 Solutions

Operations Research : Applications and Algorithms

Ch. 2.1 - Prob. 1P Ch. 2.1 - Prob. 2P Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - Prob. 7P Ch. 2.2 - Prob. 1P Ch. 2.3 - Prob. 1P Ch. 2.3 - Prob. 2P

Ch. 2.3 - Prob. 3P Ch. 2.3 - Prob. 4P Ch. 2.3 - Prob. 5P Ch. 2.3 - Prob. 6P Ch. 2.3 - Prob. 7P Ch. 2.3 - Prob. 8P Ch. 2.3 - Prob. 9P Ch. 2.4 - Prob. 1P Ch. 2.4 - Prob. 2P Ch. 2.4 - Prob. 3P Ch. 2.4 - Prob. 4P Ch. 2.4 - Prob. 5P Ch. 2.4 - Prob. 6P Ch. 2.4 - Prob. 7P Ch. 2.4 - Prob. 8P Ch. 2.4 - Prob. 9P Ch. 2.5 - Prob. 1P Ch. 2.5 - Prob. 2P Ch. 2.5 - Prob. 3P Ch. 2.5 - Prob. 4P Ch. 2.5 - Prob. 5P Ch. 2.5 - Prob. 6P Ch. 2.5 - Prob. 7P Ch. 2.5 - Prob. 8P Ch. 2.5 - Prob. 9P Ch. 2.5 - Prob. 10P Ch. 2.5 - Prob. 11P Ch. 2.6 - Prob. 1P Ch. 2.6 - Prob. 2P Ch. 2.6 - Prob. 3P Ch. 2.6 - Prob. 4P Ch. 2 - Prob. 1RP Ch. 2 - Prob. 2RP Ch. 2 - Prob. 3RP Ch. 2 - Prob. 4RP Ch. 2 - Prob. 5RP Ch. 2 - Prob. 6RP Ch. 2 - Prob. 7RP Ch. 2 - Prob. 8RP Ch. 2 - Prob. 9RP Ch. 2 - Prob. 10RP Ch. 2 - Prob. 11RP Ch. 2 - Prob. 12RP Ch. 2 - Prob. 13RP Ch. 2 - Prob. 14RP Ch. 2 - Prob. 15RP Ch. 2 - Prob. 16RP Ch. 2 - Prob. 17RP Ch. 2 - Prob. 18RP Ch. 2 - Prob. 19RP Ch. 2 - Prob. 20RP Ch. 2 - Prob. 21RP Ch. 2 - Prob. 22RP

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