To solve a linear programming problem using the simplex method, we'll need the objective function and the constraints. Since the text extraction didn't work, I'll describe the general procedure and you can provide the details for your specific problem.

### General Steps for the Simplex Method:

1. **Formulate the Problem**: 
   - Identify the objective function.
   - Write down the constraints.
   
2. **Set Up the Initial Simplex Tableau**:
   - Convert the constraints into equations by adding slack variables.
   - Set up the initial tableau with the objective function and the constraints.

3. **Perform Simplex Iterations**:
   - Identify the pivot element (column and row).
   - Perform row operations to change the pivot column so that the pivot element becomes 1 and all other elements in the pivot column become 0.
   - Repeat the process until the optimal solution is reached (no more negative indicators in the objective function row for maximization problems).

### Example Problem:
Let's assume we have the following problem:

Maximize \( z = 3x_1 + 2x_2 \)

Subject to:
\[
\begin{align*}
2x_1 + x_2 &\leq 18 \\
2x_1 + 3x_2 &\leq 42 \\
3x_1 + x_2 &\leq 24 \\
x_1, x_2 &\geq 0
\end{align*}
\]

#### Step 1: Formulate the Problem
\[
\text{Maximize } z = 3x_1 + 2x_2
\]
Subject to:
\[
\begin{align*}
2x_1 + x_2 + s_1 &= 18 \\
2x_1 + 3x_2 + s_2 &= 42 \\
3x_1 + x_2 + s_3 &= 24 \\
x_1, x_2, s_1, s_2, s_3 &\geq 0
\end{align*}
\]

#### Step 2: Initial Simplex Tableau
\[
\begin{array}{c|cccccc}
 & x_1 & x_2 & s_1 & s_2 & s_3 & \text{RHS} \\
\hline
s_1 & 2 & 1 & 1 & 0 & 0 & 18 \\
s_2 & 2 & 3 & 0 & 1 & 0 & 42 \\
s_3 & 3 & 1 & 0 & 0 & 1 & 24 \\
\hline
z & -3 & -2 & 0 & 0 & 0 & 0 \\
\end{array}
\]

#### Step 3: Perform Simplex Iterations
1. Identify the entering variable (most negative indicator in the \(z\)-row): \(x_1\)
2. Identify the leaving variable (smallest positive ratio of RHS to pivot column value): \(s_3\)
3. Perform row operations to make the pivot element 1 and all other elements in the pivot column 0.

(Continue the iterations until optimal solution is reached).

Since I don't have the exact problem details from the image, please provide the objective function and constraints. I'll guide you through the specific steps for your problem.

Learn how to solve linear programming problems using the simplex method. This detailed guide covers formulating the problem, setting up the initial simplex tableau, and performing simplex iterations. Suitable for advanced mathematics students and professionals.

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