Suppose $C(x)=x^{2}-6 x+16$ represents the costs, in hundreds, to produce $x$ thousand pens. How many pens should be produced to minimize the cost? What is the minimum cost?

Number of pens to minimize cost: pens

Minimum cost: dollars

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Step 1 ：The cost function is a quadratic function. The minimum point of a quadratic function \(f(x) = ax^2 + bx + c\) is given by \(-\frac{b}{2a}\). In this case, \(a=1\) and \(b=-6\).

Step 2 ：So, the number of pens to minimize cost can be found by calculating \(-\frac{b}{2a}\).

Step 3 ：The minimum cost can be found by substituting the number of pens that minimize cost into the cost function.

Step 4 ：By substituting the values, we get the number of pens as \(3000\) and the minimum cost as \(700\).

Step 5 ：Final Answer: The number of pens to minimize cost is \(\boxed{3000}\) and the minimum cost is \(\boxed{700}\).