Consider the economic input-output system shown in Problem 10.6. Suppose the energy consumptions of the three sectors are t₁ = 100 MJ/$, t₂ = 500 MJ/$, and t₃ = 200 MJ/$. 

1. Calculate the life cycle energy consumption per dollar of final demand for each sector. 

2. Calculate the energy return on investment for sector 1, given that the price of energy produced from this sector is $2 per joule.

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10.6 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 x; 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, aij = xij/xj. 3. Use the model derived above to determine the throughput from each sector for final demands fi = $100, f2 = $300, f3 = $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.