**Cost Function and Average Variable Cost Calculation**A company's cost function is given by the equation:\[ TC = 25 + 30Q + 0.2Q^2 \]The task is to determine the equation for the company's average variable cost (AVC).**Options:**1. $ \text{AVC} = 25Q + 30 + 0.2Q $2. $ \text{AVC} = 30 + 0.4Q $3. $ \text{AVC} = 25 + 30Q + 0.4Q^2 $4. $ \text{AVC} = 30 + 0.2Q $5. $ \text{AVC} = 30Q + 0.2Q^2 $**Solution Approach:**To find the average variable cost, we must first isolate the variable portion of the total cost (TC) and divide it by the quantity (Q). The variable cost is represented by the parts of the TC that change with Q, which are $30Q + 0.2Q^2$. The fixed cost is the constant term, 25, and does not affect the AVC.Thus, we calculate AVC as:\[\text{AVC} = \frac{30Q + 0.2Q^2}{Q} = 30 + 0.2Q\]Hence, the correct equation for the average variable cost is **Option 4: $ \text{AVC} = 30 + 0.2Q $**.

Variable cost refers to the cost which changes with change in the level of output. The fixed cost…

Answered: A company's cost function is given as:…

A company's cost function is given as: TC = 25+ 30Q + 0.2Q² What is the equation for the company's average variable cost? Select one: O AVC= 25Q + 30+ 0.2Q

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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**Cost Function and Average Variable Cost Calculation**

A company's cost function is given by the equation:

\[ TC = 25 + 30Q + 0.2Q^2 \]

The task is to determine the equation for the company's average variable cost (AVC).

**Options:**

1. $ \text{AVC} = 25Q + 30 + 0.2Q $
2. $ \text{AVC} = 30 + 0.4Q $
3. $ \text{AVC} = 25 + 30Q + 0.4Q^2 $
4. $ \text{AVC} = 30 + 0.2Q $
5. $ \text{AVC} = 30Q + 0.2Q^2 $

**Solution Approach:**

To find the average variable cost, we must first isolate the variable portion of the total cost (TC) and divide it by the quantity (Q). The variable cost is represented by the parts of the TC that change with Q, which are $30Q + 0.2Q^2$. The fixed cost is the constant term, 25, and does not affect the AVC.

Thus, we calculate AVC as:

\[
\text{AVC} = \frac{30Q + 0.2Q^2}{Q} = 30 + 0.2Q
\]

Hence, the correct equation for the average variable cost is **Option 4: $ \text{AVC} = 30 + 0.2Q $**.

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