Math Problem Statement
Solution
Let's solve the missing values in the table step by step.
Given Information:
- Fixed Cost (FC) remains constant across all outputs.
- Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC)
- Average Cost (AC) = Total Cost (TC) / Output
- Marginal Cost (MC) = Change in Total Cost (ΔTC) / Change in Output (ΔQ)
Step 1: Identify the Fixed Cost (A)
From the given values, FC remains constant across outputs except for the first row where it's missing.
Observing the table:
- When Output = 3, FC = 20.
- When Output = 4, FC = 20.
Since FC does not change, A = 20.
Step 2: Find B
From the Total Cost formula: For Output = 2: We will solve for E later.
Since FC is constant, B = 20.
Step 3: Find C
For Output = 3:
Step 4: Find D
For Output = 6: We will solve for E later.
Step 5: Find E
For Output = 2: For Output = 6: We will solve for D in the next step.
Step 6: Find D
Observing the TC trend:
- TC for Output = 5 is 300.
- MC from Output = 5 to 6 is J.
Since Marginal Cost (MC) is:
For Output = 6:
We'll compute this after finding J.
Step 7: Find G
Step 8: Find H
Step 9: Find J
Marginal Cost from Output 5 to 6:
We'll solve once E is known.
Would you like a detailed breakdown for each value? Let me know! Here are some related questions:
- How do we calculate Marginal Cost for each output level?
- Why does Fixed Cost remain the same across different outputs?
- What is the significance of Average Cost in decision-making?
- How does the cost function in Question 2 relate to the given table?
- What happens if Variable Costs increase significantly?
Tip: Always double-check Fixed Costs first, as they remain unchanged across outputs.
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Math Problem Analysis
Mathematical Concepts
Cost Analysis
Fixed Cost
Variable Cost
Total Cost
Average Cost
Marginal Cost
Formulas
Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC)
Average Cost (AC) = Total Cost (TC) / Output
Marginal Cost (MC) = Change in Total Cost (ΔTC) / Change in Output (ΔQ)
Theorems
-
Suitable Grade Level
High School (Grades 11-12)
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