1. **Problem Statement:** We are given inequalities from the transportation problem: (2) 5 – x ≥ 0 (3) 5 – y ≥ 0 (4) 8 – (x + y) ≥ 0 (5) x + y – 4 ≥ 0 We need to rewrite these inequalities by separating variables on the left and constants on the right. 2. **Rewrite each inequality:** - For (2): $$5 - x \geq 0$$ Subtract 5 from both sides: $$5 - x - 5 \geq 0 - 5$$ Simplify: $$-x \geq -5$$ Multiply both sides by $-1$ (remember to reverse inequality): $$\cancel{-}x \leq \cancel{-}5$$ $$x \leq 5$$ - For (3): $$5 - y \geq 0$$ Subtract 5 from both sides: $$5 - y - 5 \geq 0 - 5$$ Simplify: $$-y \geq -5$$ Multiply both sides by $-1$ (reverse inequality): $$\cancel{-}y \leq \cancel{-}5$$ $$y \leq 5$$ - For (4): $$8 - (x + y) \geq 0$$ Distribute minus: $$8 - x - y \geq 0$$ Subtract 8 from both sides: $$8 - x - y - 8 \geq 0 - 8$$ Simplify: $$-x - y \geq -8$$ Multiply both sides by $-1$ (reverse inequality): $$\cancel{-}x + \cancel{-}y \leq \cancel{-}8$$ $$x + y \leq 8$$ - For (5): $$x + y - 4 \geq 0$$ Add 4 to both sides: $$x + y - 4 + 4 \geq 0 + 4$$ Simplify: $$x + y \geq 4$$ 3. **Final inequalities:** $$x \leq 5$$ $$y \leq 5$$ $$x + y \leq 8$$ $$x + y \geq 4$$ These inequalities define the feasible region for the transportation problem. **Answer:** (2) $x \leq 5$ (3) $y \leq 5$ (4) $x + y \leq 8$ (5) $x + y \geq 4$