Business The change in the size of businesses in a certain Canadian city from one year to the next can he described by a Markov chain. The businesses are classified into three categories based on size: small (2-10 employees), medium (11—43 employees), and large (44 or more employees). The transition matrix for a 1-year period is given below.
Suppose that in 2015, there were 2094 small, 2363 medium, and 2378 large businesses. Based on this model, find the number of businesses of each type that would be expected in each of the following years. Source: Applied Statistics.
(a) 2016 (b) 2017
(c) Write the transition matrix for a 2-year period.
Based on your answer to part (c), what percent of medium businesses are in each of the following categories after 2 years?
(d) Small businesses (e) Large businesses
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Finite Mathematics (11th Edition)
- Consider a game where you need to fill a 5-digit number by spinning a wheel. Every time you spin the wheel a random digit shows up between 0 – 9 with equal probability. You are to decide where to place the digit in your number. Once you choose a location for the digit you cannot change it. Your objective is to maximize the number you get. (a) Set this up as a Markov Decision Process, identify the states, actions, and transition matrices.arrow_forwardA car rental company has two locations. Each week, 80% of the cars rented at location A are returned to location A and the rest location B. Of the cars rented at location B, 30% are returned to location B by the end of the week and the rest to location A. a. Make a transition diagram for this process. b. Write the transition matrix T for this process. cIf 50% of the company's cars start this week at location A, and 50% at location B, find the proportion of cars that will be at each location one week later Label your answers. d. Write and solve a system of equations to find the stable distribution (correct to 3 decimal places) for this Markov process. Show all calculations and label the row operations.arrow_forwardA study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The following transition matrix represents the transition probabilities from one state to another. Elec. Gas Oil Solar Electricity 0.60 0.05 0.10 Natural Gas 0.15 0.85 0.10 0.06 Fuel Oil 0.10 0.02 0.75 0.06 Solar Energy 0.15 0.08 0.05 0.88 Among homeowners within the area, 20% currently use electricity, 35% use natural gas, 40% use oil, and 5% use solar energy as the major source of heat for their homes. In the long run, what percentage of homeowners within the area will be using solar energy as their major source of heating fuel? (Round your answer to one decimal place. Assume the trend continues.) 12.2 X %arrow_forward
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