Step 1 :The revenue of the company when selling 1000 pens is calculated by multiplying the selling price of each pen (\$10) by the number of pens sold (1000). So, \(R = 10 \times 1000 = 10000\).
Step 2 :The cost of producing 1000 pens is calculated by multiplying the cost of producing each pen (\$2) by the number of pens produced (1000) and adding the one-time start-up cost (\$6500). So, \(C = 2 \times 1000 + 6500 = 8500\).
Step 3 :The profit is calculated by subtracting the cost from the revenue. So, \(P = R - C = 10000 - 8500 = 1500\).
Step 4 :\(\boxed{1500}\) is the profit when the company sells 1000 pens.