There are three brands of soft drink: A, B and C. After month of advertising, it

Question

There are three brands of soft drink: A, B and C. After month of advertising, it was discovered that of the A drinkers, 20% had switched to B and 10% switched to C. Of the B drinkers, 5% had switch to A and 25% to C. Of the C drinkers, 10% had switched to A and 15% to B. Assume at the beginning 15,000 people drank A, 20,000 people drank B and 45,000 people drank C.

A) Set up a stochastic matrix to show the change between brands A, B and C

B) After one month, how many were now drinking A, B and C, respectively?

C) Assuming the advertising is repeated monthly, and the switches in allegiance are consistent with what is described above, find the steady state matrix of this scenario to one decimal-place accuracy.

D) Based on your result in part C, which soft drink has the most drinkers? State this figure.

Explanation / Answer

Softdrink C has most drinkers.

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