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 $C(x)=0.4 x^{2}-96 x+16,541$. What is the minimum unit cost?
Do not round your answer.
Unit cost:

Step 1 ：The unit cost $C$ is given by the function $C(x)=0.4 x^{2}-96 x+16,541$.

Step 2 ：The minimum unit cost corresponds to the minimum point of the function $C(x)$.

Step 3 ：This is a quadratic function, and the minimum point of a quadratic function $ax^2 + bx + c$ is given by $-\frac{b}{2a}$.

Step 4 ：In this case, $a = 0.4$ and $b = -96$. So, we need to calculate $-\frac{b}{2a}$.

Step 5 ：Substitute $a = 0.4$ and $b = -96$ into the formula $-\frac{b}{2a}$, we get $x = 120.0$.

Step 6 ：Substitute $x = 120.0$ into the function $C(x)$, we get $C = 10781.0000000000$.

Step 7 ：\(\boxed{10781}\) is the minimum unit cost.