A publishing company has determined that a new edition of an existing mathematics textbook will be readopted by 80% of its current users and will be adopted by 7% of the users of other texts if the text is not changed radically. To determine whether it should change the book radically to attract more sales, it uses Markov chains. Assume that the text in question currently has 25% of its possible market.
(a) Create the transition matrix for this chain.
(b) Find the probability vector for the text three editions later and, from that, determine the percent of the market for that future edition.
(c) Find the steady-state vector for this text to determine what percent of its market this text will have if this policy is continued.