Solving a linear programming problem with mixed constraints (some constraints of type ≤ and some of type ≥) can be done using the Big-M method. The Big-M method is an extension of the Simplex method that allows for the inclusion of inequality constraints in the linear programming problem.

The Big-M method involves introducing artificial variables and a large positive constant (M) to convert the inequality constraints into equality constraints. The basic steps involved in solving a linear programming problem with mixed constraints using the Big-M method are as follows:

1. Formulate the linear programming problem with the objective function and the given constraints.
2. Convert the inequality constraints into equality constraints by introducing slack variables for the ≤ constraints and surplus variables for the ≥ constraints.
3. Introduce artificial variables for each constraint that has a type ≥. These artificial variables are used to ensure feasibility of the initial basic feasible solution.
4. Add the artificial variables to the objective function with a coefficient of M (large positive constant) to discourage their presence in the solution.
5. Solve the modified linear programming problem using the Simplex method to obtain an initial basic feasible solution.
6. If the optimal solution obtained has an artificial variable with a non-zero value, it indicates that the original problem is infeasible. Otherwise, proceed to the next step.
7. Remove the artificial variables from the objective function and re-optimize the linear programming problem using the Simplex method to obtain the final optimal solution.

The Big-M method allows for the inclusion of both type ≤ and type ≥ constraints by introducing artificial variables and a large positive constant. It ensures that all constraints are satisfied while finding the optimal solution to the linear programming problem. Thus, the correct answer to the given question is option 'A' - Big-M method.