中五數學一問(線性規劃)

(a) 已完成(b)(i) z = 100 - x - y(ii) 6x + 5y + 4(100 - x - y) = 2x + y + 400(iii) 按條件得400x + 600y + 400(100 - x - y) >= 44000...(1)800x + 200y + 400(100 - x - y) >= 48000...(2)x + y <= 100...(3)整理後得y >= 20...(1)2x - y >= 40...(2)x + y <= 100...(3)(iv) 陰形區域的三個頂點為(30,20), (80,20), (140/3, 160/3)分別代入2x + y + 400 可得當x = 30, y = 20, z = 50時有最小I成本值480