The Fashion Store has $\$ 12,000$ available each month for advertising. Newspaper ads cost $\$ 400$ apiece and no more than 30 can be run per month. Radio ads cost $\$ 200$ each and no more than 40 can run per month. TV ads cost $\$ 1600$ a piece, with a maximum of 7 available each month. Approximately 2000 women will see each newspaper ad, 1600 will hear each radio ad, and 15,000 will see each TV ad. How much of each type of advertising should be used if the store wants to maximize exposure? How many newspaper ads should be placed?

Step 1 ：Define the variables: Let the number of newspaper ads be denoted as x, the number of radio ads as y, and the number of TV ads as z.

Step 2 ：Set up the objective function: The function to be maximized is the total exposure, which is given by \(2000x + 1600y + 15000z\).

Step 3 ：Set up the constraints: The constraints are given by the budget and the maximum number of ads that can be run per month. These are: \(400x + 200y + 1600z \leq 12000\) (budget constraint), \(x \leq 30\) (maximum number of newspaper ads), \(y \leq 40\) (maximum number of radio ads), and \(z \leq 7\) (maximum number of TV ads).

Step 4 ：Solve the linear programming problem: Using these constraints and the objective function, we can solve the problem to find the optimal number of each type of ad to run.

Step 5 ：Interpret the solution: The solution to the problem indicates that the store should place approximately \(\boxed{0}\) newspaper ads to maximize exposure.