https://file.aiquickdraw.com/mathbot/file/1738664987026nytg17aj.jpg

The given mathematical problem is a **Linear Programming Problem (LPP)** that aims to **maximize** the objective function:

\[
Z = X_1 + 4X_2
\]

**Subject to the constraints:**

\[
2X_1 + X_2 \leq 3
\]
\[
3X_1 + 5X_2 \leq 9
\]
\[
X_1 + 3X_2 \leq 5
\]
\[
X_1, X_2 \geq 0
\]

### Solution Approach:
To solve this LPP, we can use:
1. **Graphical Method** (if there are two variables)
2. **Simplex Method** (if constraints make graphical approach difficult)
3. **Solver tools** like MATLAB, Excel, or Python's `scipy.optimize`.

Would you like a graphical solution, or should I solve it using the simplex method?  

---

### Related Questions:
1. How do we plot the feasible region for this LPP?
2. What is the significance of slack variables in simplex method?
3. How do we identify corner points in graphical solutions?
4. How can we apply duality in this LPP?
5. How do we interpret sensitivity analysis in linear programming?

**Tip:** In graphical methods, always find the **feasible region** first before calculating the optimal solution.

max z = x1 + 4x2, subject to 2x1 + x2 <= 3, 3x1 + 5x2 <= 9, x1 + 3x2 <= 5, x1, x2 >= 0

This problem focuses on solving a linear programming problem with the objective to maximize z = x1 + 4x2 subject to constraints. The solution involves finding the feasible region and optimizing the objective function. Suitable for students in Grades 11-12 or college-level courses.

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