An input-output model consists of the following flows in dollars: x₁₁ = 10, x₁₂ = 20, x₂₁ = 30, x₂₂= 10. The throughputs are x₁= 50 and x₂ = 40, and the emissions of CO₂ from sectors 1 and 2 are 50 kg and 100 kg, respectively. Answer the following questions for this system. 

1. Determine the final demand and value added for each sector. 

2. Determine the direct requirements matrix. 

3. For final demands ƒ₁ = 10 and ƒ₂= 10, determine the throughputs.