The production cost $C(x) = 2x^2 - 40x + 300$ represents a quadratic function. Since the coefficient of $x^2$ is positive (2), the parabola opens upwards, meaning it has a minimum point.

To find the minimum production cost, we need to determine the vertex of the parabola. For a quadratic function in the form $ax^2 + bx + c$, the x-coordinate of the vertex is given by:

$x = \frac{-b}{2a}$

In this case:

• $a = 2$
• $b = -40$

Substituting into the vertex formula:

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