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 \(\boxed{700}\).