Leontief model is used to analyze the interdependence of conomies. In this model you consider n industries in which the output of each industry is needed as put for other industries and perhaps for the industry itself. In this model input must equal output. hat is, the amount paid by each equals the amount received by each. This situation can be represented with an input output n x n matrix. uppose in a far away land of Eigenbazistan, in a small and remote country town called Matrixville, here lived a Farmer, a Tailor, a Carpenter, a Coal Miner and Slacker Bob. The Farmer produced food; he Tailor, clothes; the Carpenter, housing; the Coal Miner supplied energy; and Slacker Bob made ligh Quality 100 Proof Moonshine, half of which he drank himself. The following is the input-output natrix for the small community. Farmer 0.25 0.15 0.25 0.18 0.20 0.15 0.28 0.18 0.17 0.05 Tailor Carpenter Coal Miner 0.22 0.19 0.22 0.22 0.10 0.20 0.15 0.20 0.28 0.15 Slacker Bob 0.18 0.23 0.15 0.15 0.50 o for example, the Carpenter consumes 22% of all food, 19% of all clothes, 22% of all housing, 22% f all energy and 10% of all High Quality 100 Proof Moonshine. Now, let pF, PT, PC, PCM,PSB denote he incomes of the Farmer, Tailor, Carpenter, Coal Miner and Slacker Bob, respectively. Note that ach of these quantities not only denotes the incomes of each of our esteemed citizens, but also the cost f the corresponding goods, in other words the system is closed. So for example, pF is the Farmer's come as well as the cost of all the food. So if the Farmer produces $100 worth of food, then his come will also be $100 since all of this food is bought out and the profits go to the Farmer. he Farmer output will be pF, but to produce that output he will need: 0.25pF +0.15pT+0.25pc + 18PCM + PSB0.20 The idea is, of course, to be able to figure out how should we price the goods in der for the citizens of Matrixville to survive; i.e. we must find pF, PT, PC, PCM,PSB. Write down a stem of equations that describe the business happening in Matrixville. Call the matrix of coefficients 1. What are the highest and the lowest priced commodities in Matrixville?