A remote city has an industrial system consisting of Farmers, Carpenters, and Tailors. o The total output of the farmers is divided as follows: 20% to farmers, 50% to carpentersand 30% to tailors. I The total output of the carpenters is divided as follows: None to carpenters, 30% tofarmers, 70% to tailors. I The total output of the tailors is divided as follows: 30% to farmers, 40% to carpenters,30% to tailors. (a) (6 pts)
If the total annual output of the farmers, carpenters, and tailors in 2012 were 40,30, and 20 million dollars, respectively, what will be their total output after one year?Compute it. In the next two parts you are either going to write a matrix product or a matrix equation.You will not compute anything! Assume that the total annual output (in million dollars)of the farmers, carpenters, and tailors in 2012 were pp, pg, and pg", respectively. (b) (6 pts) What will be their total output value after two years? Write a matrix productwhich would illustrate the answer. (c) (3 pts) Setup a matrix equation that would enable us to ﬁnd equilibrium prices that makeeach sector’s income (namely total annual output) match it’s expenditure if possible.
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