Consider the network shown in Figure 10.15. It consists of three sectors (nodes) and shows the monetary exchange between the sectors. The final demand and value added flows are shown as flows to and from human resources. Assuming this diagram to represent a static snapshot of the network, answer the following questions. 

1. Represent the network as an input-output table and find the total throughput r; for each sector. 

2. Determine the input-output model relating the total throughput from each sector x; to the final demand fi. This will require you to find the appropriate coefficients, a_ij = x_ij/x_j. 

3. Use the model derived above to determine the throughput from each sector for final demands ƒ₁ = $100, ƒ₂ = $300,ƒ₃ = $0. 

4. From the results obtained in (3), prepare the corresponding network diagram or input-output table. You will need to show the monetary flows between all the sectors and human resources.

                                                                               

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0.22 m³ natural gas 0.49 kg coal 0.4 kg CO₂ Production of high voltage electricity at plant from natural gas 1 kg CO₂ Production of high voltage electricity at plant from coal 1kWh HV electricity, NG 200 100 1kWh HV electricity, coal 1 load clean dishes 0.25 kWh HV electricity, NG 0.75 kWh HV electricity coal 1.0 kWh Operation of dishwasher cycle LV electricity Figure 10.14 Life cycle inventory modules relevant to a glass cup. 500 200 0.09 m³ natural gas 200 100 200 3 300 2 400 800 900 HV electricity mix stepped down to LV distribution line 100 Figure 10.15 Input-output network. All flows are in dollars. Manufacture of glassware 50 2 g NOx 350 150 0.9 kWh HV electricity, NG 1 unit glass cup