A supply company manufactures copy machines. The unit cost \( C \) (the cost in dollars to make each copy machine) depends on the number of machines made. If \( x \) machines are made, then the unit cost is given by the function \( C(x)=1.2 x^{2}-264 x+19,560 \), How many machines must be made to minimize the unit cost? Do not round your answer.

To minimize the unit cost \( C(x) = 1.2x^{2} - 264x + 19,560 \), you can use the vertex formula of a parabola, which is given by \( x = -\frac{b}{2a} \). Here, \( a = 1.2 \) and \( b = -264 \). Plugging in these values: \[ x = -\frac{-264}{2 \cdot 1.2} = \frac{264}{2.4} = 110 \] Thus, to minimize the unit cost, 110 machines must be made. Also, check the unit cost calculation by evaluating \( C(110) \) for practical insights on production efficiency and cost-effectiveness—a great way to ensure your calculations lead to real-world savings!