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The question involves calculating the total cost of producing 140 units of a product, given the marginal cost function and fixed costs. The marginal cost per unit produced is provided as:

\[
\text{Marginal cost} = \frac{2500 \ln(q + 30)}{(q + 30)^2}
\]

where $ q $ is the quantity of units produced, and the fixed costs are $2000.

### Steps to Solve the Problem:
1. **Find the Total Cost**:
   The total cost $ C(q) $ is obtained by integrating the marginal cost function over $ q $, and then adding the fixed costs.
   
   \[
   C(q) = \int \frac{2500 \ln(q + 30)}{(q + 30)^2} dq + \text{fixed costs}
   \]

2. **Evaluate for $ q = 140 $**:
   Once the integral is computed, substitute $ q = 140 $ to find the total cost for producing 140 units.

3. **Add Fixed Costs**:
   Add the fixed cost of $2000 to the result of the integral to get the total cost.

I will calculate the integral and evaluate the result. Let's proceed.The total cost function obtained by integrating the marginal cost is:

\[
C(q) = -\frac{2500 \ln(q + 30)}{q + 30} - \frac{2500}{q + 30} + C_0
\]

where $ C_0 $ is the constant of integration.

Next, we will determine the total cost for $ q = 140 $, adding the fixed cost of $2000.

Let's compute this value.The total cost of producing 140 units is approximately **$1910**, when rounded to the nearest dollar. This includes the fixed cost of $2000.

Let me know if you'd like further details or clarifications!

Here are five related questions:
1. How would the cost change if the number of units produced was 200 instead of 140?
2. What is the role of the logarithmic function in the marginal cost equation?
3. How do fixed costs influence the total cost as the number of units increases?
4. Can the marginal cost function be simplified or approximated for large values of $ q $?
5. What is the economic significance of integrating the marginal cost function?

**Tip**: When integrating marginal cost functions, always remember to include fixed costs in your final total cost calculation!

A company has a marginal cost per unit of its product given by: 2500 ln(q + 30) / (q + 30)^2, where q is the quantity of units produced. Fixed costs are $2000. Find the total cost of producing 140 units, rounding to the nearest integer.

This problem involves calculating the total cost for a company producing 140 units using a marginal cost function. It includes integration and fixed costs of $2000. Suitable for university students studying calculus.

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