RESEARCH OPERATION

QUESTION TWO The table below shows an analysis of brand preferences for three brands of beverages sold in a supermarket. i. ii. BRANDS Fanta only Mirinda only Pepsi only Fanta to Pepsi Fanta to Mirinda Required: iii. Mirinda to Fanta. Mirinda to Pepsi Pepsi to Fanta Pepsi to Mirinda Total NUMBER OF CONSUMERS PERCENTAGE 114 32 18 5 13 14 48 50 65 12 5 32 16 360 8ASNE I 18 9 100 Determine the brand insistence and switching rates and hence prepare a probability transition matrix representing the above information. Given that this month the market shares for the three brands, i.e. Fanta Pepsi and Mirinda are 30%, 45% and 25% respectively, what will be the expected market shares for the three brands after 2 months? Calculate the steady state probabilities if and when the system settles down. (20 marks)