The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below is the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands.

a) What is the market share of Brand D in the long run?.

b) How many customers will shift preference in using Brand C soap in the long run?

c) What is the mean return time of Brand 1?

d) What is the percentage change of Brand B?

From/To A B D A B C D 0.2 0.3 0.1 0.4 0 0.2 0.5 0.3 0.3 0.5 0 0.2 0.3 0.4 0.3 0 Number of Customers 2300 2800 2500 2400