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The problem provides the marginal cost function of a company, given by:

\[
MC(q) = \frac{4000 \ln(q + 30)}{(q + 30)^2}
\]

where $ q $ represents the number of units produced. The fixed costs are stated to be $2000.

We are asked to find the total cost of producing 150 units, which involves integrating the marginal cost function over the production interval and adding the fixed costs.

### Step-by-step plan:

1. **Integrate the marginal cost function** from $ q = 0 $ to $ q = 150 $ to get the variable cost.
2. **Add the fixed cost** of $2000 to the result from step 1.
3. **Round the total cost** to the nearest whole number.

Let me calculate that for you.The total cost of producing 150 units is approximately **2449 dollars** when rounded to the nearest whole number.

Would you like further details or explanations on any part of this process?

Here are five related questions that expand on this topic:
1. How does the marginal cost function change with respect to $ q $?
2. What role do fixed costs play in total cost calculations?
3. Can you derive the formula for total cost if the marginal cost function is given?
4. How would the total cost change if the number of units produced was increased to 200?
5. What is the economic significance of the marginal cost curve?

**Tip:** Understanding how to integrate marginal cost functions helps you analyze the total production cost over a range of outputs.

Una empresa tiene un costo marginal por unidad de su producto producido dado por: (4000 ln(q + 30)) / (q + 30)^2. Los costos fijos son de 2000 dólares. El costo de producir 150 artículos es (redondear a un entero):

Find the total cost of producing 150 units for a company, given the marginal cost function MC(q) = (4000 ln(q + 30)) / (q + 30)^2 and fixed costs of 2000 dollars. This detailed step-by-step solution involves integration of the marginal cost function and is suitable for college-level students.

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