An advertising company wants to attract new customers by placing a total of at most 9 ads in 3 newspapers. Each ad in the Sentinel costs $\$ 200$ and will be read by 2,000 people. Each ad in the Journal costs $\$ 100$ and will be read by 500 people. Each ad in the Tribune costs $\$ 50$ and will be read by 1,000 people. The company wants at least 11,000 people to read its ads. How many ads should it place in each paper in order to minimize the advertising costs? What is the minimum cost? Construct a mathematical model in the form of a linear programming problem. Use $x_{1}$ to represent the number of ads placed in the Sentinel, $x_{2}$ to represent the number of ads placed in the Journal, and $x_{3}$ to represent the number of ads placed in the Tribune.

Step 1 ：First, we need to set up the constraints for the problem. The total number of ads placed in all three newspapers cannot exceed 9, so we have the constraint \(x_{1} + x_{2} + x_{3} \le 9\).

Step 2 ：Next, we need to ensure that at least 11,000 people read the ads. This gives us the constraint \(2000x_{1} + 500x_{2} + 1000x_{3} \ge 11000\).

Step 3 ：Since the number of ads cannot be negative, we also have the constraints \(x_{1} \ge 0\), \(x_{2} \ge 0\), and \(x_{3} \ge 0\).

Step 4 ：The objective function to minimize is the total cost of the ads, which is \(200x_{1} + 100x_{2} + 50x_{3}\).

Step 5 ：Now, we can solve this linear programming problem using a method such as the simplex method or graphical method. However, since this problem only involves three variables, we can also solve it by inspection.

Step 6 ：By inspection, we can see that placing all 9 ads in the Tribune will reach 9,000 people, which is not enough. Placing 8 ads in the Tribune and 1 ad in the Sentinel will reach 10,000 people, which is still not enough. Placing 7 ads in the Tribune and 2 ads in the Sentinel will reach 11,000 people, which meets the requirement.

Step 7 ：The cost of placing 7 ads in the Tribune and 2 ads in the Sentinel is \(7*50 + 2*200 = 350 + 400 = 750\) dollars.

Step 8 ：By checking other combinations, we can see that no other combination can reach at least 11,000 people with a lower cost. Therefore, the company should place 2 ads in the Sentinel and 7 ads in the Tribune to minimize the advertising costs.

Step 9 ：The minimum cost is \(\boxed{750}\) dollars.