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電子課本網(wǎng) 第139頁

第139頁

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解: (1)根據(jù)表格可得$\begin{cases}3000m + 4000n = 17000\\4000m + 3000n = 18000\end{cases},$解得$\begin{cases}m = 3\\n = 2\end{cases}。$$\therefore m$的值為3,$n$的值為2。
(2)當(dāng)$0<x\leq200$時,店主獲得海鮮串的總利潤$y=(5 - 3)x = 2x;$當(dāng)$200<x\leq400$時,店主獲得海鮮串的總利潤$y=(5 - 3)\times200+(5\times0.8 - 3)(x - 200)=x + 200。$$\therefore y=\begin{cases}2x(0<x\leq200)\\x + 200(200<x\leq400)\end{cases}。$
(3)設(shè)降價后獲得肉串的總利潤為$z$元,令$W = z - y。$$\because200<x\leq400,$$\therefore y = x + 200。$又$\because z=(3.5 - a - 2)(1000 - x)=(a - 1.5)x + 1500 - 1000a,$$\therefore W = z - y=(a - 2.5)x + 1300 - 1000a。$$\because0<a<1,$$\therefore a - 2.5<0,$$\therefore W$隨$x$的增大而減小,當(dāng)$x = 400$時,$W$的值最小。由題意可得$z\geq y,$$\therefore W\geq0,$即$(a - 2.5)\times400 + 1300 - 1000a\geq0,$解得$a\leq0.5。$$\therefore a$的最大值為0.5。
解: (1)若從$A$城運往$C$鄉(xiāng)農(nóng)機$x$臺,則從$A$城運往$D$鄉(xiāng)農(nóng)機$(30 - x)$臺,從$B$城運往$C$鄉(xiāng)農(nóng)機$(34 - x)$臺,從$B$城運往$D$鄉(xiāng)農(nóng)機$[40 - (34 - x)]$臺,$\therefore W = 250x + 200(30 - x)+150(34 - x)+240[40 - (34 - x)]=140x + 12540。$又$\because\begin{cases}x\geq0\\30 - x\geq0\\34 - x\geq0\\40 - (34 - x)\geq0\end{cases},$$\therefore0\leq x\leq30,$$\therefore W$關(guān)于$x$的函數(shù)表達式為$W = 140x + 12540(0\leq x\leq30,$且$x$為整數(shù)$)。$
(2)要使$W\geq16460,$即$140x + 12540\geq16460,$解得$x\geq28。$又$\because0\leq x\leq30,$$\therefore28\leq x\leq30,$且$x$為整數(shù),$\therefore$有3種不同的調(diào)運方案:①當(dāng)$x = 28$時,從$A$城運往$C$鄉(xiāng)28臺,運往$D$鄉(xiāng)2臺,從$B$城運往$C$鄉(xiāng)6臺,運往$D$鄉(xiāng)34臺;②當(dāng)$x = 29$時,從$A$城運往$C$鄉(xiāng)29臺,運往$D$鄉(xiāng)1臺,從$B$城運往$C$鄉(xiāng)5臺,運往$D$鄉(xiāng)35臺;③當(dāng)$x = 30$時,從$A$城運往$C$鄉(xiāng)30臺,運往$D$鄉(xiāng)0臺,從$B$城運往$C$鄉(xiāng)4臺,運往$D$鄉(xiāng)36臺。
(3)$\because$從$A$城運往$C$鄉(xiāng)的農(nóng)機的運費每臺減免$a$元,$\therefore W = x(250 - a)+200(30 - x)+150(34 - x)+240[40 - (34 - x)]=(140 - a)x + 12540。$$\because a\leq200,$$\therefore$需對$a$進行討論。①當(dāng)$0<a<140,$即$140 - a>0$時,$W$隨$x$的增大而增大,當(dāng)$x = 0$時,$W$取最小值,此時的方案為從$A$城運往$C$鄉(xiāng)0臺,運往$D$鄉(xiāng)30臺,從$B$城運往$C$鄉(xiāng)34臺,運往$D$鄉(xiāng)6臺;②當(dāng)$a = 140$時,$W = 12540$為定值,此時$x$只需滿足$0\leq x\leq30,$且$x$為整數(shù)即可,共有31種不同的方案,每種方案總費用一樣;③當(dāng)$140<a\leq200,$即$140 - a<0$時,$W$隨$x$的增大而減小,當(dāng)$x = 30$時,$W$取最小值,此時的方案為從$A$城運往$C$鄉(xiāng)30臺,運往$D$鄉(xiāng)0臺,從$B$城運往$C$鄉(xiāng)4臺,運往$D$鄉(xiāng)36臺。