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Solve the given linear programming problem using the table method. The table of basic solutions is provided. Maximize P= 15x, + 8x2 subject to x, + X2 56 X, + 4x2 s 12 X1, X2 2 0 S2 Feasible? 12 Yes -12 No 0. 3. Yes 0. 6. Yes 12 No 4 Yes r6030수0

Solve the given linear programming problem using the table method. The table of basic solutions is provided. Maximize P= 15x, + 8x2 subject to x, + X2 56 X, + 4x2 s 12 X1, X2 2 0 S2 Feasible? 12 Yes -12 No 0. 3. Yes 0. 6. Yes 12 No 4 Yes r6030수0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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### Solving Linear Programming Problem Using the Table Method #### Problem Statement Maximize \( P = 15x_1 + 8x_2 \) subject to: \[ x_1 + x_2 \leq 6 \] \[ x_1 + 4x_2 \leq 12 \] \[ x_1, x_2 \geq 0 \] #### Table of Basic Solutions | \( x_1 \) | \( x_2 \) | \( s_1 \) | \( s_2 \) | Feasible? | |:---------:|:---------:|:---------:|:---------:|:---------:| | 0 | 0 | 6 | 12 | Yes | | 0 | 6 | 0 | -12 | No | | 0 | 3 | 3 | 0 | Yes | | 6 | 0 | 0 | 6 | Yes | | 12 | 0 | -6 | 0 | No | | 4 | 2 | 0 | 0 | Yes | 1. **Basic Solutions:** - The table lists various combinations of \( x_1 \) and \( x_2 \) that are evaluated to check feasibility against the given constraints. 2. **Constraints and Slack Variables:** - \( s_1 \) and \( s_2 \) represent slack variables for the constraints \( x_1 + x_2 \leq 6 \) and \( x_1 + 4x_2 \leq 12 \), respectively. These variables account for any unused resources in the constraints. 3. **Feasibility:** - Feasible solutions are those that satisfy all the constraints \( x_1 + x_2 \leq 6 \), \( x_1 + 4x_2 \leq 12 \) and \( x_1, x_2 \geq 0 \). By examining the table, we identify the feasible solutions as: - \( (x_1, x_2) = (0, 0) \) - \( (x_1, x_2) = (0, 3) \) -
Transcribed Image Text:### Solving Linear Programming Problem Using the Table Method #### Problem Statement Maximize \( P = 15x_1 + 8x_2 \) subject to: \[ x_1 + x_2 \leq 6 \] \[ x_1 + 4x_2 \leq 12 \] \[ x_1, x_2 \geq 0 \] #### Table of Basic Solutions | \( x_1 \) | \( x_2 \) | \( s_1 \) | \( s_2 \) | Feasible? | |:---------:|:---------:|:---------:|:---------:|:---------:| | 0 | 0 | 6 | 12 | Yes | | 0 | 6 | 0 | -12 | No | | 0 | 3 | 3 | 0 | Yes | | 6 | 0 | 0 | 6 | Yes | | 12 | 0 | -6 | 0 | No | | 4 | 2 | 0 | 0 | Yes | 1. **Basic Solutions:** - The table lists various combinations of \( x_1 \) and \( x_2 \) that are evaluated to check feasibility against the given constraints. 2. **Constraints and Slack Variables:** - \( s_1 \) and \( s_2 \) represent slack variables for the constraints \( x_1 + x_2 \leq 6 \) and \( x_1 + 4x_2 \leq 12 \), respectively. These variables account for any unused resources in the constraints. 3. **Feasibility:** - Feasible solutions are those that satisfy all the constraints \( x_1 + x_2 \leq 6 \), \( x_1 + 4x_2 \leq 12 \) and \( x_1, x_2 \geq 0 \). By examining the table, we identify the feasible solutions as: - \( (x_1, x_2) = (0, 0) \) - \( (x_1, x_2) = (0, 3) \) -
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