1. **Problem statement:** We want to find the number of turkeys ($x$) and hams ($y$) to distribute such that: - $x \leq 600$ (max turkeys available) - $y \leq 800$ (max hams available) - $x + y \geq 1200$ (at least 1200 total items) We have two objectives: **(a) Minimize cost:** Cost function is $C = 12x + 14y$. **(b) Maximize value:** Value function is $V = 22x + 20y$. --- 2. **Constraints:** $$ \begin{cases} x \leq 600 \\ y \leq 800 \\ x + y \geq 1200 \\ x \geq 0, y \geq 0 \end{cases} $$ 3. **Minimizing cost:** We want to minimize $C = 12x + 14y$ subject to the constraints. 4. **Maximizing value:** We want to maximize $V = 22x + 20y$ subject to the same constraints. --- 5. **Feasible region:** Since $x + y \geq 1200$, and $x \leq 600$, $y \leq 800$, the possible points are on or above the line $x + y = 1200$ within the rectangle $0 \leq x \leq 600$, $0 \leq y \leq 800$. 6. **Vertices of feasible region:** - Point A: $(600, 600)$ since $600 + 600 = 1200$ and both within max limits. - Point B: $(600, 800)$ max hams. - Point C: $(400, 800)$ since $400 + 800 = 1200$. 7. **Evaluate cost at vertices:** - At A: $C = 12(600) + 14(600) = 7200 + 8400 = 15600$ - At B: $C = 12(600) + 14(800) = 7200 + 11200 = 18400$ - At C: $C = 12(400) + 14(800) = 4800 + 11200 = 16000$ Minimum cost is at point A: $(600, 600)$ with cost 15600. 8. **Evaluate value at vertices:** - At A: $V = 22(600) + 20(600) = 13200 + 12000 = 25200$ - At B: $V = 22(600) + 20(800) = 13200 + 16000 = 29200$ - At C: $V = 22(400) + 20(800) = 8800 + 16000 = 24800$ Maximum value is at point B: $(600, 800)$ with value 29200. --- **Final answers:** - Min cost: distribute 600 turkeys and 600 hams, cost = 15600. - Max value: distribute 600 turkeys and 800 hams, value = 29200.