Introduction:
The given linear programming problem is a maximization problem with two variables A and B. The objective function is to maximize Z = 2A + 3B, subject to the constraint A ≤ B.

Explanation:
To solve this linear programming problem, we can use the simplex method. The simplex method is an iterative procedure that systematically improves the solution until an optimal solution is reached.

Steps of the Simplex Method:
1. Formulate the problem: Write the objective function and constraints in standard form.
2. Create the initial tableau: Set up the initial tableau by converting the objective function and constraints into equations.
3. Select the pivot column: Choose the column with the most negative coefficient in the objective row as the pivot column.
4. Select the pivot row: Divide the right-hand side of each constraint by the corresponding entry in the pivot column. Choose the row with the smallest positive ratio as the pivot row.
5. Perform row operations: Use row operations to make the pivot element equal to 1 and all other elements in the pivot column equal to 0.
6. Update the tableau: Update the tableau by performing row operations on the other rows to make all other elements in the pivot column equal to 0.
7. Repeat steps 3-6: Repeat steps 3-6 until there are no negative coefficients in the objective row or there are no positive ratios in the pivot column.
8. Interpret the solution: Once the simplex method has converged, interpret the solution by reading the optimal values for the variables from the tableau.

Analysis:
In this particular linear programming problem, the constraint A ≤ B implies that the feasible region is a subset of the line A = B. The objective function Z = 2A + 3B represents a family of parallel lines with slope -2/3.

Alternative Optimal Solutions:
Since the feasible region is a subset of the line A = B, there are infinitely many points that satisfy the constraint. Therefore, there may be alternative optimal solutions that yield the same maximum value for the objective function. These alternative optimal solutions lie on the line A = B and have different values for A and B.

Conclusion:
In conclusion, the given linear programming problem may contain alternative optimal solutions due to the constraint A ≤ B. The simplex method can be used to solve this problem by iteratively improving the solution until an optimal solution is reached.