1. **State the problem:** We want to maximize an objective function subject to constraints with $x_1 > 0$ and $x_2 > 0$. However, the objective function and constraints are not fully specified in the problem statement. 2. **Clarify the problem:** To solve a maximization problem graphically, we need the objective function (e.g., maximize $Z = c_1 x_1 + c_2 x_2$) and the constraints (e.g., inequalities involving $x_1$ and $x_2$). 3. **Graphical method overview:** - Plot the constraints on the $x_1$-$x_2$ plane. - Identify the feasible region where all constraints are satisfied. - Plot the objective function as a line and move it parallel to itself to find the maximum value within the feasible region. 4. **Conclusion:** Please provide the objective function and constraints explicitly to proceed with the graphical solution.