Show the details of your formulation, including: o the definitions of the decision variables, including their units and their bounds, - the objective function and the constraints as mathematical expressions in the decision variables. Provide labels for the constraints and objective function indicating the physical meaning of each (e.g. "limit on capacity of plant 3\"), and their units. Summarize the results in terms of the original problem as though you were reporting to a manager. If the results are unusual in any way, state why this might be so. Be succinct. Each solution should require no more than a couple of pages, but must also show the details of your solution. 3. [10 marks] An economic study of the job situation in Ottawa has just been completed. The survey shows that jobs in the Ottawa area are currently distributed as follows: 40% in government, 30% in high technology, and 30% in services. The study also includes forecasts of future job distributions, which are based on a Markov chain model of single-year job migration between sectors shown in the following table (table entries are in percent). to High technology ENE mum. a) What percent of Ottawa jobs will be in each sector 1, 2, and 3 years from now? b) What is the expected distribution of jobs by sector at steady state? What is expected to happen in the services sector (will it grow or shrink)