1. **Problem statement:** A zoo keeper wants to fence a rectangular habitat for goats. The length $L$ should be at least 80 feet, and the perimeter $P$ should be no more than 300 feet. 2. **Define variables:** Let $L$ = length and $W$ = width of the habitat. 3. **Write inequalities:** - Length at least 80 feet: $$L \geq 80$$ - Perimeter no more than 300 feet: $$2L + 2W \leq 300$$ 4. **Simplify perimeter inequality:** $$2L + 2W \leq 300$$ Divide both sides by 2: $$\cancel{2}L + \cancel{2}W \leq \frac{300}{\cancel{2}}$$ $$L + W \leq 150$$ 5. **System of inequalities:** $$\begin{cases} L \geq 80 \\ L + W \leq 150 \end{cases}$$ 6. **Graph description:** - The region includes all points where $L$ is at least 80 (to the right of vertical line $L=80$). - And points below or on the line $L + W = 150$. - The feasible region is the intersection of these two. 7. **Possible solutions:** - i. $L=80$, $W=70$ (since $80 + 70 = 150$) - ii. $L=90$, $W=50$ (since $90 + 50 = 140 \leq 150$) - iii. $L=100$, $W=40$ (since $100 + 40 = 140 \leq 150$) Final answer: $$\boxed{\begin{cases} L \geq 80 \\ L + W \leq 150 \end{cases}}$$ Possible solutions: $(80,70), (90,50), (100,40)$