### Solving Linear Programming Problem Using the Table Method#### Problem StatementMaximize $ 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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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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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