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antomehmet
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Suppose that in the city of Shenzhen there are three polluters (say, paper mills).
Currently each polluter emits 900 units of NOX per year (E1 = E2 = E3 = 900).
These polluters are currently not subject to emissions control, i.e., zero
abatement (A1 = A2 = A3 = 0). Their total abatement cost functions are given by
Polluter 1: C1(A1) = A
2
1
1
4
+ 100
Polluter 2: C2(A2) = A
2
2
1
2
+ 90
Polluter 3: C3(A3) =
A
2
3
3
4
+ 80
As a result of the NOX emissions, people in the city of Shenzhen suffer from
asthma. Suppose that the city’s target NOX emission level is E = E1 + E2 + E3 =
1,600. Thus the three polluters must jointly reduce their emission level by A =
A1 + A2 + A3 =1,100 units.
Q2. Using the Lagrangian method, derive the abatement levels for the three
polluters A1*, A2*, and A3* that will minimise the total abatement cost for the city.
Step 1: Set up the Lagrangian optimisation problem. (2 points)
Currently each polluter emits 900 units of NOX per year (E1 = E2 = E3 = 900).
These polluters are currently not subject to emissions control, i.e., zero
abatement (A1 = A2 = A3 = 0). Their total abatement cost functions are given by
Polluter 1: C1(A1) = A
2
1
1
4
+ 100
Polluter 2: C2(A2) = A
2
2
1
2
+ 90
Polluter 3: C3(A3) =
A
2
3
3
4
+ 80
As a result of the NOX emissions, people in the city of Shenzhen suffer from
asthma. Suppose that the city’s target NOX emission level is E = E1 + E2 + E3 =
1,600. Thus the three polluters must jointly reduce their emission level by A =
A1 + A2 + A3 =1,100 units.
Q2. Using the Lagrangian method, derive the abatement levels for the three
polluters A1*, A2*, and A3* that will minimise the total abatement cost for the city.
Step 1: Set up the Lagrangian optimisation problem. (2 points)
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Hi there,
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While you're waiting for an answer, did you know we have 300,000 study resources that could answer your question in TSR's Learn together section?
We have everything from Teacher Marked Essays to Mindmaps and Quizzes to help you with your work. Take a look around.
If you're stuck on how to get started, try creating some resources. It's free to do and can help breakdown tough topics into manageable chunks. Get creating now.
Thanks!
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