A farmer is going to divide her 30 acre farm between two crops. Seed for crop A costs $\$ 25$ per acre. Seed for crop B costs $\$ 50$ per acre. The farmer can spend at most $\$ 1000$ on seed. If crop B brings in a profit of $\$ 200$ per acre, and crop A brings in a profit of $\$ 130$ per acre, how many acres of each crop should the farmer plant to maximize her profit?

Step 1 ：Let's denote the area of crop A as x and the area of crop B as y.

Step 2 ：The constraints are: \(x + y \leq 30\) (the total area should not exceed 30 acres) and \(25x + 50y \leq 1000\) (the total cost of the seeds should not exceed $1000).

Step 3 ：The objective function to maximize is the total profit, which is \(130x + 200y\).

Step 4 ：We can solve this problem using linear programming, which minimizes a linear objective function subject to linear equality and inequality constraints. Since we want to maximize the profit, we can change the sign of the coefficients in the objective function to make it a minimization problem.

Step 5 ：The result shows that the optimal solution is to plant 20 acres of crop A and 10 acres of crop B. This will bring in a maximum profit of $4600.

Step 6 ：Final Answer: The farmer should plant \(\boxed{20}\) acres of crop A and \(\boxed{10}\) acres of crop B to maximize her profit.