Florida Generation owns two generating units with the following cost curve: C_ =15+1.4P, +0.04P; $/h, C, = 25 + 1.6P, + 0.02P; S/h, 50 sP, <150 200
Florida Generation owns two generating units with the following cost curve: C_ =15+1.4P, +0.04P; $/h, C, = 25 + 1.6P, + 0.02P; S/h, 50 sP, <150 200
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Help with this problem
![**Power Generation Cost Optimization**
Florida Generation owns two generating units with the following cost curves:
For unit A:
\[ C_A = 15 + 1.4P_A + 0.04P_A^2 \quad \text{\$/h}, \quad 50 \le P_A \le 150 \]
For unit B:
\[ C_B = 25 + 1.6P_B + 0.02P_B^2 \quad \text{\$/h}, \quad 200 \le P_B \le 500 \]
The company needs to supply a demand of 400 MW. Power can also be purchased from the wholesale power market at a market clearing price of $15/MWh.
**Tasks:**
1. Determine the optimal production level for each unit, \( P_A \) and \( P_B \), and the optimal amount of power \( P_M \) to be purchased from the wholesale market.
2. Compute the total cost to supply this demand.
This involves finding the cost-effective balance between generating power internally through units A and B or purchasing additional power from the market. The mathematical challenge is to minimize costs while meeting the specific demand constraints.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf39397d-cff1-4eb1-98e5-06c79e9fa8b7%2F7ece7500-aff7-4342-8ffe-cb6eff1b88ff%2Fhxll02b_processed.png&w=3840&q=75)
Transcribed Image Text:**Power Generation Cost Optimization**
Florida Generation owns two generating units with the following cost curves:
For unit A:
\[ C_A = 15 + 1.4P_A + 0.04P_A^2 \quad \text{\$/h}, \quad 50 \le P_A \le 150 \]
For unit B:
\[ C_B = 25 + 1.6P_B + 0.02P_B^2 \quad \text{\$/h}, \quad 200 \le P_B \le 500 \]
The company needs to supply a demand of 400 MW. Power can also be purchased from the wholesale power market at a market clearing price of $15/MWh.
**Tasks:**
1. Determine the optimal production level for each unit, \( P_A \) and \( P_B \), and the optimal amount of power \( P_M \) to be purchased from the wholesale market.
2. Compute the total cost to supply this demand.
This involves finding the cost-effective balance between generating power internally through units A and B or purchasing additional power from the market. The mathematical challenge is to minimize costs while meeting the specific demand constraints.
Expert Solution
Step 1
A cost curve is a graph representing the production costs as a function of the total amount produced in economics. A cost curve is the consequence of productively efficient enterprises optimizing their production process by minimizing cost consistent with each potential level of production in a free market economy.
Step by step
Solved in 2 steps
Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education