Math Problem Statement

Find the value of letters A, B, C, D, E, F, G, H, I, and J in the given cost table.

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: TC=FC+VCTC = FC + VC For Output = 2: E=B+160E = B + 160 We will solve for E later.

Since FC is constant, B = 20.

Step 3: Find C

For Output = 3: TC=FC+VCTC = FC + VC 210=20+C210 = 20 + C C=190C = 190

Step 4: Find D

For Output = 6: E=20+DE = 20 + D We will solve for E later.

Step 5: Find E

For Output = 2: E=20+160=180E = 20 + 160 = 180 For Output = 6: E=20+DE = 20 + D 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: MC=ΔTCΔQMC = \frac{\Delta TC}{\Delta Q}

For Output = 6: D=TC620D = TC_6 - 20

We'll compute this after finding J.

Step 7: Find G

G=E2=1802=90G = \frac{E}{2} = \frac{180}{2} = 90

Step 8: Find H

H=3005=60H = \frac{300}{5} = 60

Step 9: Find J

Marginal Cost from Output 5 to 6: J=E30065J = \frac{E - 300}{6 - 5}

We'll solve once E is known.

Would you like a detailed breakdown for each value? Let me know! Here are some related questions:

  1. How do we calculate Marginal Cost for each output level?
  2. Why does Fixed Cost remain the same across different outputs?
  3. What is the significance of Average Cost in decision-making?
  4. How does the cost function in Question 2 relate to the given table?
  5. 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

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Suitable Grade Level

High School (Grades 11-12)