The given marginal cost function is:

$C(x) = 3x^2 - 140x + 2900$

To minimize the marginal cost, we need to find the critical points by taking the derivative of the function and setting it equal to zero.

1. Take the derivative of $C(x)$ with respect to $x$: $C'(x) = \frac{d}{dx}(3x^2 - 140x + 2900)$

2. Set $C'(x) = 0$ to find the critical points.

Let me calculate this.The critical point is $x = \frac{70}{3} \approx 23.33$.

Therefore, the company should produce approximately 23 or 24 units to minimize the marginal cost.

Would you like further details or clarification?

Here are 5 related questions you could explore:

1. What is the value of the marginal cost at the minimum point?
2. How does the second derivative test confirm that this is a minimum?
3. What happens to the marginal cost if the company produces more than the optimal number of units?
4. How is the behavior of this quadratic cost function related to real-world production costs?
5. What does the constant term in the cost function represent?

Tip: When minimizing cost functions, always check the second derivative to confirm whether the critical point is a minimum or maximum.