The given cost function is $C(x) = 28x^2 - 371x + 3125$, where $C$ represents the cost in dollars, and $x$ is the number of cell phones produced (in thousands).

To find the number of units that minimizes the cost, we need to calculate the value of $x$ that minimizes this quadratic function.

Steps:

1. The cost function is a quadratic equation in the form: $C(x) = ax^2 + bx + c$ where $a = 28$, $b = -371$, and $c = 3125$.

2. For any quadratic function $ax^2 + bx + c$, the value of $x$ that minimizes (or maximizes) the function is given by: $x = -\frac{b}{2a}$

3. Substituting the values of $a$ and $b$: $x = -\frac{-371}{2(28)} = \frac{371}{56} \approx 6.63$

Thus, the company should produce approximately 6.63 thousand cell phones (or 6630 units) to minimize the cost.

Would you like more details, or do you have any further questions?

Here are 5 related questions for deeper understanding:

1. What is the significance of the coefficients in the cost function?
2. How can you verify whether this value of $x$ truly minimizes the cost function?
3. What is the cost at the minimum production level?
4. How does the second derivative test confirm the minimum?
5. Can this model be extended to predict costs for different production levels?

Tip: The vertex formula $x = -\frac{b}{2a}$ is useful for finding the minimum or maximum of any quadratic function.