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its expected costs. Example1 A car Rental Company ? In analyzing the historical records it is determined that 60% of the cars rented in Orlando are returned to Orlando, whereas 40% end up in Tampa. ? Of the cars rented from Tampa office ,70% are returned to Tampa, whereas 30% end up in Orlando. Example1 A car Rental Company Orlando Tampa 40% 30% 60% 70% Example1 A car Rental Company ? Develop a model. ? Let n represents the number of business days. ? Define On=the number of cars in Orlando at the end of day n Tn=the number of cars in Tampa at the end of day n Example1 A car Rental Company ? Thus we have: 110 . 6 0 . 30 . 4 0 . 7n n nn n nO O TT O T?????????Example1 A car Rental Company ? Equilibrium values ? The equilibrium values for the system are those values of On and Tn for which no change in the system takes place. ? Let’s call the equilibrium values, if exists, O and T. Then 11nnnnO O OT T T??????Example 4 Voting Tendencies ? Presidential voting tendencies are of interest every 4 years. During the past decade, the Independent party has emerged as viable alternate for voters in the presidential race. Example 4 Voting Tendencies ? Let’s consider a threeparty system with Republicans, Democrats, and Independents. Problem Identification ? Can we find the longterm behavior of voters in a presidential election? Assumptions ? During the past decade, the trends have been to vote less strictly along party lines. ? Hypothetical historical data for voting trends in the past 10 years of statewide voting Republican Democrats Independents Republican Democrats Independents Model Identification nD ?the number of voters to vote democratic in period n nR ?the number of voters to vote republican in period n nI ?the number of voters to vote independent in period n