Solve Linear Programming Problem by big-M method :

Maximise Z=3X_1+2X_2+〖3X〗_3

subjected to constraints

2X_1+X_2+X_3≤2

                                    3X_1+4X_2+2X_3≥8;           X_1,X_2,X_3≥0

Let's solve the given Linear Programming Problem using the **Big-M method** step by step.

### Problem
**Maximize:**
\[
Z = 3X_1 + 2X_2 + 3X_3
\]

**Subject to:**
\[
2X_1 + X_2 + X_3 \leq 2
\]
\[
3X_1 + 4X_2 + 2X_3 \geq 8
\]
\[
X_1, X_2, X_3 \geq 0
\]

### Step 1: Convert inequalities

Solve Linear Programming Problem by big-M method:
Maximize Z = 3X_1 + 2X_2 + 3X_3
subject to the constraints:
2X_1 + X_2 + X_3 ≤ 2
3X_1 + 4X_2 + 2X_3 ≥ 8; X_1, X_2, X_3 ≥ 0

Solve a linear programming problem using the Big-M method. Maximize Z = 3X_1 + 2X_2 + 3X_3 subject to constraints 2X_1 + X_2 + X_3 ≤ 2 and 3X_1 + 4X_2 + 2X_3 ≥ 8. This detailed solution includes step-by-step explanations on handling inequalities and non-negativity constraints using the Big-M method.

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