Linear Inequalities

Concept:Constraints are inequalities derived from limited machine hours.Explanation:For machine $M_1$: each chair takes 3 hours, each table takes 3 hours, total available 36 hours, so $3x + 3y \leq 36$ which simplifies to $x + y \leq 12$.For machine $M_2$: each chair takes 5 hours, each table takes 2 hours, total available 50 hours, so $5x + 2y \leq 50$.Also $x \geq 0$ and $y \geq 0$ because quantities cannot be negative.Answer:$x + y \leq 12$, $5x + 2y \leq 50$, $x \geq 0$, $y \geq 0$This matches option B.