Answer Happy

1.6 Applications of Linear Systems 71 1.6 EXERCISES 1. Suppose an economy has only two sectors, Goods and Ser vices. Each year, Goods sells 80% of its output to Services and keeps the rest, while Services selle 70% of its output to Goods and retains the rest. Find equilibrium prices for the annual outputs of the Goods and Services sectors that make cach sector's income match its expenditures unbalanced cquation is B,S,+HO -- HBO, + HS For each compound, construct a vector that is the mumbers of atoms of boron, solfur, hydrogen, and oxygen] 6. When solutions of sodium phosphate and burium fitrateure mixed, the result is barium phosphate as a precipitate) and sodium nitrate. The unbalanced equation is Na ,,+BNO) -- Ba(PO-NANO, For each compound, construct a vector that lists them hers of stoms of sodium (Na), phosphorus, orygen, burim and nitrogen. For instance, burium nitrate corresponds to (0,0,6.1.2) Goods Services 2. Find another set of equilibrium prices for the economy in Example 1. Suppose the same economy used Japanese yen instead of dollars to measure the value of the various sec tors' outputs. Would this change the problem in any way? Discuss 3. Consider an economy with three sectors. Chemicals & Met- als, Foels & Power, and Machinery, Chemicals sells 30% 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% to Chemicals and 40% to Fuels and retains the rest . Construct the exchange table for this economy b. Develop a system of equations that leads to prices at which cach sector's income matches its expenses. Then write the augmented matrix that can be row reduced to find these prices c. IM Find a set of equilibrium prices when the price for the Machinery output is 100 units. 4. Suppose an economy has four sectors, Agriculture (A). En ergy (E). Manufacturing (M), and Transportation (T) Sector A sells 10% of its output to Eand 25 to M and retains the restSector Esells 30% of its output to A.35 to M and 25% to T and retains the rest. Sector Msells 30% of its output to A. 15 to E, and 40% to T and retains the rest. Sector Tsells 20% of its output to A, 105 to E, and 30% to M and retains the rest a. Construct the exchange table for this economy b. [M] Find a set of equilibrium prices for the economy. Balance the chemical equations in Exercises 5-10 mising the vector equation approach discussed in this section 5. Boron sallide reacts violently with water to form boric acid and hydrogen sulfide gas (the smell of rotten eges). The 7. Alka-Seltzer contains sodium bicarbonate NaHCO) and citric acid CH CH.0). When a tablet is divind in water the following reaction produces sodium citrate, water, and carbon dioxide (g: NaHCO,+H.C.H.O. - Na.C.H.0, 1.000, 8. The following reaction between potassium permanganate (KMnO) and manganese sulfate in water produces man ganese dioxide, potassium sulfate, and sulfuric acit KMUO. + MnSO. + HO - MO, K.50+H 50 For each compound, construct a vector that is the numbers of atoms of potassium (K), manganese, oxygen sulfur, and hydrogen 9. IM If possible, use exact arithmetic or rational format for calculations in balancing the following chemical reaction: PhN+Cr MnO,- Pb, 0, +C+MnO, + NO 10. [M] The chemical reaction below can be used in some indus- trial processes, such as the production of arsene (AH). Lise exact arithmetic or rational format for calculations to balance this equation Mus+ As Cross+H.SO - HMnO, + Ass+C5,0-HO 11. Find the general flow pattern of the network shown in the figure. Assuming that the flows are all nonnegative, what is the largest possible value for xy? 12. Find the general traffic pattern in the freeway network shown in the figure. (Flow rates are in caminte b. Describe the general tradic patter when the road whose flow is is closed