A medical equipment industry manufactures $\mathrm{X}$-ray machines. The unit cost $C$ (the cost in dollars to make each $\mathrm{X}$-ray machine) depends on the number of machines made. If $x$ machines are made, then the unit cost is given by the function $C(x)=1.1 x^{2}-440 x+49,720$. What is the minimum unit cost? Do not round your answer. Unit cost: $\$ \llbracket$

Step 1 ：The unit cost is given by a quadratic function \(C(x)=1.1x^2 - 440x + 49720\).

Step 2 ：The minimum unit cost will occur at the vertex of the parabola represented by this function.

Step 3 ：The x-coordinate of the vertex of a parabola given by \(f(x) = ax^2 + bx + c\) is \(-b/2a\).

Step 4 ：We substitute \(a = 1.1\) and \(b = -440\) into this formula to find the x-coordinate of the vertex, which will give us the number of machines that results in the minimum unit cost.

Step 5 ：We find that the x-coordinate of the vertex is approximately 200.

Step 6 ：We then substitute this x-coordinate back into the function \(C(x)\) to find the minimum unit cost.

Step 7 ：We find that the minimum unit cost is approximately $5720.00 when 200 machines are made.

Step 8 ：Final Answer: The minimum unit cost is \(\boxed{5720.00}\) dollars.