Linear Inequalities

Concept:We set variables for quantities from each food source and write inequalities for minimum requirements and non-negativity.Explanation:Let $x_1$ be the quantity (in units) from place $A$, and $x_2$ from place $B$.Carbohydrate from $A$ is $4x_1$, from $B$ is $3x_2$; total must be at least $50$: $4x_1 + 3x_2 \ge 50$.Protein from $A$ is $5x_1$, from $B$ is $3x_2$; total must be at least $40$: $5x_1 + 3x_2 \ge 40$.Quantities cannot be negative: $x_1 \ge 0$, $x_2 \ge 0$.Answer:Option A: $4x_1 + 3x_2 \ge 50$, $5x_1 + 3x_2 \ge 40$, $x_1 \ge 0$, $x_2 \ge 0$.