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This problem asks for the **entering variable** in a Simplex tableau. Here's how to determine it step by step:

### Analysis:
1. **Entering variable** is determined by the most negative coefficient in the **Z row** of the tableau. These coefficients represent the rates of increase in the objective function (Z) for the corresponding variables \(x_1\), \(x_2\), etc.

2. From the Z row:
   - Coefficient of \(x_1\): \(-3\)
   - Coefficient of \(x_2\): \(-4\)

3. The **most negative value** is \(-4\), which corresponds to \(x_2\).

### Conclusion:
The entering variable is **\(x_2\)**.

Would you like further details about why this works or how the Simplex method proceeds from this point? 

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Here are five related questions to consider:
1. What is the next step after identifying the entering variable in the Simplex method?
2. How do we determine the leaving variable in the tableau?
3. What would happen if there were no negative coefficients in the Z row?
4. How does the Simplex method handle unbounded solutions?
5. Can an entering variable be selected differently in certain optimization problems?

**Tip:** In the Simplex method, always verify the Z row before proceeding to ensure you’re moving toward optimality.

The table below is a formulation of a linear programming problem to be solved using simplex. What will be the entering variable for the table given? (the Z row is the objective function).

Learn how to determine the entering variable in a Simplex tableau for linear programming problems. This step-by-step solution explains how to identify the most negative coefficient in the Z row to proceed toward optimization.

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