Should this have a slack variable? Answer: Answer: The LP in standard form is: \begin{align*} \text{minimize} \quad & 3x_1 - x_2 \\ \text{s.t.} \quad & x_1 + x_2 + x_3 = 1 \\ & 2x_1 - x_2 - x_4 + x_3 = 2 \\ & x_1, x_2, x_3, x_4 \geq 0 \end{align*} Explanation: The standard form of a linear programming problem is: \begin{align*} \text{minimize} \quad & c^T x \\ \text{s.t.} \quad & Ax = b \\ & x \geq 0 \end{align*} where \(c\) and \(x\) are vectors of coefficients, \(A\) is a matrix of coefficients, and \(b\) is a vector of constants. In the given problem, the first constraint is already in the standard form. The second constraint is an inequality, so we need to convert it into an equality. We do this by introducing a slack variable \(x_4\). The inequality \(2x_1 - x_3 \geq x_2 - 2\) can be rewritten as \(2x_1 - x_2 - x_4 + x_3 = 2\), where \(x_4 \geq 0\). This ensures that the equality holds when \(x_4 = 0\), and the inequality holds when \(x_4 > 0\). The non-negativity constraints \(x_1, x_2 \geq 0\) are already in the standard form. We also add the non-negativity constraint for the new variable \(x_4\)