A grocery store consumer market in a midwest city involves a competition for market shares among...

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A grocery store consumer market in a midwest city involves a competition for market shares among two grocery stores: Schnuks (Sch) and Meijers (Mjr). A consumer survey revealed that at the moment Schnuks has 60% of the market and Meijers has 40%. Moreover, each month 68% of Schnuks shoppers change to Meijers and 90% of Meijers shoppers change to Schnuks. a) What are transition matrix and initial market shares vector for this grocery store market? Sch Mjr T = to Sch to Mjr So = .6 4 Sch Mjr b) Compute the two month market share vector S2 (accurate to four decimal places) and report the percentage market shares (accurate to two decimal places) at the end of two months: S Therefore, after two months Schnuks has % of the market and Meijers has %. c) Find the exact stable vector for this Markov process (with fraction entries x/y in lowest terms) and report the long time percentage market shares (accurate to two decimal places). Sstable = Therefore, after a long enough time, Schnuks has % of the market and Meijers has %. d) Find the exact stable matrix (with fraction entries x/y in lowest terms) and the approximate stable matrix (accurate to four decimals), and find the number of months that the process takes to stabilize. SM exact = SM approx The Markov process will stabilize at month A grocery store consumer market in a midwest city involves a competition for market shares among two grocery stores: Schnuks (Sch) and Meijers (Mjr). A consumer survey revealed that at the moment Schnuks has 60% of the market and Meijers has 40%. Moreover, each month 68% of Schnuks shoppers change to Meijers and 90% of Meijers shoppers change to Schnuks. a) What are transition matrix and initial market shares vector for this grocery store market? Sch Mjr T = to Sch to Mjr So = .6 4 Sch Mjr b) Compute the two month market share vector S2 (accurate to four decimal places) and report the percentage market shares (accurate to two decimal places) at the end of two months: S Therefore, after two months Schnuks has % of the market and Meijers has %. c) Find the exact stable vector for this Markov process (with fraction entries x/y in lowest terms) and report the long time percentage market shares (accurate to two decimal places). Sstable = Therefore, after a long enough time, Schnuks has % of the market and Meijers has %. d) Find the exact stable matrix (with fraction entries x/y in lowest terms) and the approximate stable matrix (accurate to four decimals), and find the number of months that the process takes to stabilize. SM exact = SM approx The Markov process will stabilize at month