Question

1. the following graph shows the feasible region for which system of inequalities?

options:

• $y < 4, x \geq 0, x \leq 4$, and $y \geq 1$
• $y < 4, x \geq 0, x \geq 4$, and $y \leq 1$
• $y \leq 4, x \geq 0, x \geq 4$, and $y \geq 1$
• $y > 4, x \geq 0, x \leq 4$, and $y \leq 1$

Explanation:

Step1: Analyze vertical boundaries

The feasible region is between $x=0$ (solid line, $x\geq0$) and $x=4$ (solid line, $x\leq4$).

Step2: Analyze horizontal boundaries

The feasible region is between $y=1$ (solid line, $y\geq1$) and $y=4$ (dashed line, $y<4$).

Step3: Match to options

Combine the inequalities to match the correct system.

Answer:

$y < 4, x \geq 0, x \leq 4$, and $y \geq 1$