https://file.aiquickdraw.com/mathbot/file/17300923657881mgqwbgd.jpg

To solve this problem, let’s break down each part:

### Given:
The total cost (TC) function is:
\[
TC = 0.3Q^3 - 7Q^2 + 105Q + 120
\]

### Part (a): Fixed Cost
The fixed cost in a total cost function is the constant term, as it does not change with the quantity \( Q \).

In this function:
\[
\text{Fixed Cost} = 120
\]

So, **Answer** for (a) is: **120**

### Part (b): Marginal Cost (MC)
The marginal cost (MC) is the derivative of the total cost function \( TC \) with respect to \( Q \).

1. **Differentiate each term** in the TC function:
   \[
   \frac{d}{dQ}(0.3Q^3) = 0.9Q^2
   \]
   \[
   \frac{d}{dQ}(-7Q^2) = -14Q
   \]
   \[
   \frac{d}{dQ}(105Q) = 105
   \]
   The derivative of the constant term \(120\) is \(0\).

2. **Combine the results** to find the marginal cost:
   \[
   MC = 0.9Q^2 - 14Q + 105
   \]

So, **Answer** for (b) is:
\[
MC = 0.9Q^2 - 14Q + 105
\]

Would you like more details on each step, or have any other questions?

### Related Questions:
1. What is the interpretation of marginal cost in economic terms?
2. How would the fixed cost change if the TC function had no constant term?
3. What does the degree of each term in the TC function indicate about cost behavior?
4. How would you find the average cost (AC) from this TC function?
5. Can the marginal cost ever be negative, and what would that mean?

**Tip:** When calculating marginal cost, always take the derivative of the total cost function with respect to quantity (Q), as it represents the rate of change of total cost.

Given the total cost function: TC = 0.3Q^3 - 7Q^2 + 105Q + 120. 
(a) How much is the fixed cost? 
(b) Derive an equation for Marginal Cost.

Learn how to determine the fixed cost and derive the marginal cost equation from the total cost function: TC = 0.3Q^3 - 7Q^2 + 105Q + 120. Understand core concepts such as fixed costs, marginal costs, and the use of derivatives in economics. Suitable for undergraduate students studying economics or business.

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