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To find all basic feasible solutions (BFS) for the given system of linear equations: \[ \begin{aligned} 2x_1 + x_2 - x_3 + 2x_4 &= 2 \\ 3x_1 + 2x_2 + x_3 + 4x_4 &= 3 \end{aligned} \] with non-negativity constraints: \[ x_1, x_2, x_3, x_4 \geq 0 \] we follow these steps: ### Step 1: Identify Basic and Non-Basic Variables A basic feasible solution (BFS) is obtained by setting \( n - m = 4 - 2 = 2 \) variables to zero and solving for the remaining two (basic) variables. We systematically choose pairs of basic variables and solve for their values. ### Step 2: Compute BFS for Different Choices of Basic Variables We solve the system for different choices of basic variables while ensuring ____ __________ ____ _____ ___ ________ ____ ______ ________ _________ __________.
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