### 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:- \( (x_1, x_2) = (0, 0) \)- \( (x_1, x_2) = (0, 3) \)-

Name: ### Solving Linear Programming Problem Using the Table Method#### Pro
Uploaded: 2024-03-20T07:07:26.000Z
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Description: ### 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| \( x_1 \) | \( x_2 \) | \(