A vehicle factory manufactures cars. The unit cost $C$ (the cost in dollars to make each car) depends on the number of cars made. If $x$ cars are made, then the unit cost is given by the function $C(x)=0.3 x^{2}-192 x+40,357$. What is the minimum unit cost?
Do not round your answer.

Step 1 ：The problem is asking for the minimum unit cost of manufacturing cars in a vehicle factory. The unit cost $C$ (the cost in dollars to make each car) depends on the number of cars made. If $x$ cars are made, then the unit cost is given by the function $C(x)=0.3 x^{2}-192 x+40,357$.

Step 2 ：The minimum unit cost corresponds to the minimum value of the function $C(x)$. This is a quadratic function, and the minimum value of a quadratic function $ax^2 + bx + c$ occurs at $x = -\frac{b}{2a}$. In this case, $a = 0.3$ and $b = -192$, so we can substitute these values into the formula to find the number of cars that results in the minimum unit cost.

Step 3 ：Substituting $a = 0.3$ and $b = -192$ into the formula $x = -\frac{b}{2a}$, we get $x = 320.0$.

Step 4 ：We can then substitute this value of $x$ back into the function $C(x)$ to find the minimum unit cost. Substituting $x = 320.0$ into the function $C(x)=0.3 x^{2}-192 x+40,357$, we get $C = 9637.00000000000$.

Step 5 ：Final Answer: The minimum unit cost is \(\boxed{9637}\).