Explanation Given: 23% of the residences of Foxtail County are apartments. 18% are condominiums or townhouses, and the balance are single-family houses. 3% of the apartment residents plan on moving to a condominium or townhouse within the next two years, and 5% plan on moving to a single family house. 1% of those who currently reside in a condominium or townhouse plan on moving to an apartment, and 11% plan on moving to a single family house; 2% of the single family house dwellers plan on moving to an apartment, and 4% plan on moving to a condominium or townhouse. Approach: Use the given data to make a transition matrix and then find the equilibrium matrix of the transition matrix. The equilibrium matrix L can be found by solving the vector equation, L T = L together with the condition that the sum of the elements of the vector L should be equal to 1. Calculation: The transition matrix for given data is, A p t s C t h S f h T = [ 0.92 0.03 0.05 0.01 0.88 0.11 0.02 0.04 0.94 ] Let, L = [ x y z ] Be a steady state vector associated with the Markov process, the condition L T = L translates into the matrix equation, [ x y z ] [ 0.92 0.03 0.05 0.01 0.88 0.11 0.02 0.04 0.94 ] = [ x y z ] [ 0.92 x + 0.01 y + 0.02 z 0.03 x + 0.88 y + 0.04 z 0.05 x + 0.11 y + 0.94 z ] = [ x y z ] Equivalently, the linear system of equations for above matrix equation is, 0.92 x + 0.01 y + 0.02 z = x 0.03 x + 0.88 y + 0.04 z = y 0.05 x + 0.11 y + 0

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ISBN: 9781305104174

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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The long-term recommendation FCCA should make.

Solution Summary: The author explains that 23% of the residences of Foxtail County are apartments, 18% are condominiums or townhouses, and the balance are single-family houses.

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