The given image presents a linear programming problem written in Persian. Here's the translation and steps to approach the solution:

Problem Statement:

Minimize:
$Z = x_1 + x_2$

Subject to:
$4x_1 + 6x_2 \leq 24$ $-2x_1 + x_2 \geq 4$ $x_1, x_2 \geq 0$

Instructions:

a) Solve the problem graphically.
b) Solve the problem using the two-phase method.
c) Solve the problem using the Big-M method.
d) Compare the optimal solutions obtained through the two-phase and Big-M methods.

Would you like me to solve a specific part or all of these? Let me know! Below are a few clarifying questions and insights to expand your understanding.

Clarifying Questions:

1. Should the graphical solution include a full plot of the constraints and feasible region?
2. Would you like step-by-step explanations of the two-phase method?
3. Do you need the detailed formulation and steps for the Big-M method?
4. Are there any specific constraints you'd like explained in detail?
5. Should I compare results only numerically or also analyze computational effort?

Tip:

For linear programming, understanding how constraints form the feasible region (e.g., via graphical analysis) helps immensely in grasping the problem intuitively.