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Consider an economy with three sectors, Chemicals & Metals, Fuels & Power, and Machinery. Chemicals sells 20% of its output to Fuels and 50% to Machinery and retains the rest. Fuels sells 80% of its output to Chemicals and 10% to Machinery and retains the rest. Machinery sells 40% of its output to Chemicals and 40% to Fuels and retains the rest. Complete parts (a) through (c) below. a. Construct the exchange table for this economy. Distribution of Output from: Chemicals Fuels Machinery Purchased by: Chemicals Fuels Machinery (Type integers or decimals.) b. Develop a system of equations that leads to prices at which each sector's income matches its expenses. Then write the augmented matrix that can be row reduced to find these prices. The first, second, and third columns of the matrix should correspond to Chemicals, Fuels, and Machinery, respectively. The augmented matrix is. (Type an integer or decimal for each matrix element.) c. Find a set of equilibrium prices when the price for the Machinery output is 10 units. PChemicals =. PFuels =. PMachinery = (Type integers or decimals rounded to the nearest tenth as needed.)