Explanation Given data: Percentage of consumers who do not currently use SoftNWash will purchase SoftNWash the next time they buy a fabric wash is 9 % . Percentage of consumers who currently use SoftNWash will purchase it the next time they buy a fabric softer is 29 % . Calculation: 9 % of the consumers who do not currently use SoftNWash will purchase SoftNWash the next time they buy a fabric wash. Therefore, the probability for the mentioned situation is, P 1 = Next purchase Current purchase = 9 % = 0.09 29 % of the consumers who currently use SoftNWash will purchase it the next time they buy a fabric softer. Therefore the probability for the mentioned situation is, P 2 = Next purchase Current purchase = 29 % = 0.29 Calculate the probability for the consumers who do not buy SoftNWash and will not buy SoftNWash the next time they buy a fabric wash. P 1 ' = 1 − P 1 Substitute 0.09 for P 1 in the above equation. P 1 ' = 1 − 0.09 = 0.91 Calculate the probability for the consumers who currently use SoftNWash but will not buy the next time they buy a fabric wash. P 2 ' = 1 − P 2 Substitute 0.29 for P 2 in the above equation. P 2 ' = 1 − 0.29 = 0.71 Hence, the transition matrix of order 2 × 2 for the above probabilities is, T = [ 0.29 0.71 0.09 0.91 ] Assume equilibrium matrix L = [ x y ] …… ( 1 ) Consider the matrix equation. L T = L Substitute [ x y ] for L and [ 0

8th Edition

ISBN: 9781305104174

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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Chapter 11.3, Problem 6E

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A long range prediction of SoftNWash’s ultimate market share, assuming that current trends continue.

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Chapter 11.3, Problem 5E

Chapter 11.3, Problem 7E

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To make: A long range prediction of SoftNWash’s ultimate market share, assuming that current trends continue.

Solution Summary: The author calculates the probability that consumers who do not currently use SoftNWash will purchase it the next time they buy a fabric wash.