Math Problem Statement

Determine the missing values and answer the questions related to the production, average cost, total cost, and marginal cost based on the table provided.

Solution

The image contains a table and some questions in Bengali related to production, average cost, total cost, and marginal cost. Here's how to interpret and solve the problem:

Given Table:

উৎপাদন (Production)গড় ব্যয় (Average Cost)মোট ব্যয় (Total Cost)প্রান্তিক ব্যয় (Marginal Cost)
13030-
224--
3-66-
420--

Step 1: Filling in the missing values

  1. For Production = 2:

    • Given Average Cost = 24.
    • Total Cost =Average Cost×Production=24×2=48= \text{Average Cost} \times \text{Production} = 24 \times 2 = 48.
  2. For Production = 3:

    • Given Total Cost = 66.
    • Average Cost =Total CostProduction=663=22= \frac{\text{Total Cost}}{\text{Production}} = \frac{66}{3} = 22.
  3. For Production = 4:

    • Given Average Cost = 20.
    • Total Cost =Average Cost×Production=20×4=80= \text{Average Cost} \times \text{Production} = 20 \times 4 = 80.

Step 2: Calculating Marginal Cost

  • Marginal Cost (MC) is the additional cost incurred by producing one more unit.

  • For Production = 2:
    MC=Total Cost at Production = 2Total Cost at Production = 1MC = \text{Total Cost at Production = 2} - \text{Total Cost at Production = 1}
    MC=4830=18MC = 48 - 30 = 18.

  • For Production = 3:
    MC=Total Cost at Production = 3Total Cost at Production = 2MC = \text{Total Cost at Production = 3} - \text{Total Cost at Production = 2}
    MC=6648=18MC = 66 - 48 = 18.

  • For Production = 4:
    MC=Total Cost at Production = 4Total Cost at Production = 3MC = \text{Total Cost at Production = 4} - \text{Total Cost at Production = 3}
    MC=8066=14MC = 80 - 66 = 14.

Final Completed Table:

উৎপাদন (Production)গড় ব্যয় (Average Cost)মোট ব্যয় (Total Cost)প্রান্তিক ব্যয় (Marginal Cost)
13030-
2244818
3226618
4208014

Answering the Questions:

  1. উৎপাদন কার্ভের ঝোঁক: The production curve shows a decreasing trend in average cost with an increase in production, which might indicate increasing returns to scale.

  2. মূল্যায়ন: The value of production may be evaluated by the decreasing marginal cost, which indicates efficiency in production.

  3. উৎপাদন স্থর: The production level at which the marginal cost starts to decrease.

  4. গড় ও প্রান্তিক ব্যয়ের সম্পর্ক: As seen in the table, when the average cost decreases, the marginal cost is also declining, which is a typical relationship in production cost analysis.

Additional Questions:

  1. What would happen to marginal cost if the total cost increased at a constant rate?
  2. How does a decrease in average cost affect the pricing strategy of a company?
  3. What is the significance of the marginal cost being lower than the average cost?
  4. How would the table change if fixed costs were introduced?
  5. How does the concept of economies of scale relate to the data in this table?

Tip: In production analysis, understanding the relationship between average and marginal costs is crucial for determining the optimal production level and pricing strategy.

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Math Problem Analysis

Mathematical Concepts

Production Cost Analysis
Marginal Cost
Average Cost

Formulas

Total Cost = Average Cost * Production
Average Cost = Total Cost / Production
Marginal Cost = Total Cost at current production - Total Cost at previous production

Theorems

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Suitable Grade Level

Grade 10-12