Find the dual of the following LPP. max 3r1 + 2x2 – *3 s.t. I - #3 > 4 201 – a2 + 3r3 = 5 3r, <4 #1, 12 > 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The problem presented is to find the dual of the given linear programming problem (LPP). The primal LPP is as follows:

**Objective Function:**
Maximize \( 3x_1 + 2x_2 - x_3 \)

**Subject to the Constraints:**
1. \( x_1 - x_3 \geq 4 \)
2. \( 2x_1 - x_2 + 3x_3 = 5 \)
3. \( 3x_1 \leq 4 \)

**Non-negativity Constraints:**
- \( x_1, x_2 \geq 0 \)

This setup involves a maximization problem with three constraints and specifies that some of the decision variables must be non-negative. The task is to transform this into its corresponding dual problem. The dual is typically a minimization problem if the primal is a maximization problem, and it involves new variables corresponding to the constraints of the primal problem.
Transcribed Image Text:The problem presented is to find the dual of the given linear programming problem (LPP). The primal LPP is as follows: **Objective Function:** Maximize \( 3x_1 + 2x_2 - x_3 \) **Subject to the Constraints:** 1. \( x_1 - x_3 \geq 4 \) 2. \( 2x_1 - x_2 + 3x_3 = 5 \) 3. \( 3x_1 \leq 4 \) **Non-negativity Constraints:** - \( x_1, x_2 \geq 0 \) This setup involves a maximization problem with three constraints and specifies that some of the decision variables must be non-negative. The task is to transform this into its corresponding dual problem. The dual is typically a minimization problem if the primal is a maximization problem, and it involves new variables corresponding to the constraints of the primal problem.
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