Use the simplex method to solve. Maximize subject to: The maximum is z = (Simplify your answers.) with z = 3x₁ + 2x₂ + 2x3 x₁ + x₂ + 2x3 ≤38 2x₁ + x2 + x3 221 x₁ ≥0, X₂ ≥0, X3 20 =when x₁ = x₂ =, and x3 = - X3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Use the simplex method to solve. Maximize subject to: The maximum is z = (Simplify your answers.) with z = 3x₁ + 2x₂ + 2x3 x₁ + x₂ + 2x3 ≤38 2x₁ + x2 + x3 221 x₁ ≥0, X₂ ≥0, X3 20 =when x₁ = x₂ =, and x3 = - X3

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### Simplex Method for Maximization Problem

This section will guide you through solving a linear programming problem using the Simplex method. 

#### Objective:
Maximize \( z = 3x_1 + 2x_2 + 2x_3 \)

#### Subject to the constraints:
1. \( x_1 + x_2 + 2x_3 \leq 38 \)
2. \( 2x_1 + x_2 + x_3 \geq 21 \)

#### With:
\( x_1 \geq 0, \; x_2 \geq 0, \; x_3 \geq 0 \)

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**Solution:**

The maximum value of \( z \) is \( \_\_\_\_ \) when:
- \( x_1 = \_\_\_\_ \)
- \( x_2 = \_\_\_\_ \)
- \( x_3 = \_\_\_\_ \)

*(Simplify your answers.)*

---

This instructional content aims to help you understand how to apply the Simplex method for solving a maximization problem in linear programming. Make sure to simplify your answers thoroughly for a clear solution.
Transcribed Image Text:--- ### Simplex Method for Maximization Problem This section will guide you through solving a linear programming problem using the Simplex method. #### Objective: Maximize \( z = 3x_1 + 2x_2 + 2x_3 \) #### Subject to the constraints: 1. \( x_1 + x_2 + 2x_3 \leq 38 \) 2. \( 2x_1 + x_2 + x_3 \geq 21 \) #### With: \( x_1 \geq 0, \; x_2 \geq 0, \; x_3 \geq 0 \) --- **Solution:** The maximum value of \( z \) is \( \_\_\_\_ \) when: - \( x_1 = \_\_\_\_ \) - \( x_2 = \_\_\_\_ \) - \( x_3 = \_\_\_\_ \) *(Simplify your answers.)* --- This instructional content aims to help you understand how to apply the Simplex method for solving a maximization problem in linear programming. Make sure to simplify your answers thoroughly for a clear solution.
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