1. **State the problem:** We need to write inequalities for the number of workers $x$ and units produced $y$ based on the conditions: - At least 100 workers: $x \geq 100$ - No more than 200 workers: $x \leq 200$ - At least 30 units per worker: $y \geq 30x$ - Workers cannot be negative: $x \geq 0$ 2. **Write the inequalities:** $$ \begin{cases} x \geq 100 \\ x \leq 200 \\ y \geq 30x \\ x \geq 0 \end{cases} $$ 3. **Explain the graph:** - The vertical lines $x=100$ and $x=200$ form boundaries for the number of workers. - The inequality $y \geq 30x$ means the units produced must be at least 30 times the number of workers. - The inequality $x \geq 0$ restricts the graph to the right half-plane. 4. **List three possible solutions:** - $x=100$, $y=3000$ (since $y \geq 30 \times 100 = 3000$) - $x=150$, $y=4500$ (since $y \geq 30 \times 150 = 4500$) - $x=200$, $y=6000$ (since $y \geq 30 \times 200 = 6000$) These satisfy all inequalities and represent valid points in the feasible region.