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.