The problem asks to calculate the firm's marginal cost of the 10th unit, given the total cost function $TC = 4q^2 + 20q + 2400$.

1. Problem Description

The problem asks to calculate the firm's marginal cost of the 10th unit, given the total cost function $TC = 4q^2 + 20q + 2400$.

2. Solution Steps

First, we need to find the marginal cost (MC) function, which is the derivative of the total cost (TC) function with respect to quantity (q).

$$MC = \frac{dTC}{dq}$$

$$MC = \frac{d(4q^2 + 20q + 2400)}{dq}$$

$$MC = 8q + 20$$

Next, substitute q = 10 into the MC function to find the marginal cost of the 10th unit.

$$MC(10) = 8(10) + 20$$

$$MC(10) = 80 + 20$$

$$MC(10) = 100$$

3. Final Answer

The marginal cost of the 10th unit is

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