實驗十三 線性規(guī)劃與程序模塊

實驗十三線性規(guī)劃與程序模塊1、求下列線性規(guī)劃問題：方法一:用LinerProgramming[c,A,b]做In[5]:=c={0.2,0.7,0.4,0.3,0.5}A={{0.3,2,1,0.6,1.8},{0.1,0.05,0.02,0.2,0.05},{0.05,0.1,0.02,0.2,0.08}}b={70,3,10}LinearProgramming[c,A,b]minf=c.%Out[5]={0.2,0.7,0.4,0.3,0.5}Out[6]={{0.3,2,1,0.6,1.8},{0.1,0.05,0.02,0.2,0.05},{0.05,0.1,0.02,0.2,0.08}}Out[7]={70,3,10}Out[8]={0.,0.,0.,39.7436,25.641}Out[9]=24.7436方法二:用ConstrainedMin來做In[10]:=ConstrainedMin[0.2x1+0.7x2+0.4x3+0.3x4+0.5x5,{0.3x1+2x2+x3+0.6x4+1.8x5≥70,0.1x1+0.05x2+0.02x3+0.2x4+0.05x5≥3,0.05x1+0.1x2+0.02x3+0.2x4+0.08x5≥10},{x1,x2,x3,x4,x5}]ConstrainedMin::deprec:ConstrainedMinisdeprecatedandwillnotbesupportedinfutureversionsofMathematica.UseNMinimizeorMinimizeinstead.More..Out[10]={24.7436,{x1→0.,x2→0.,x2→0.,x4→39.7436,x5→25.641}}方法三:用NMinimize來做In[11]:=NMinimize[{0.2x1+0.7x2+0.4x3+0.3x4+0.5x5,0.3x1+2x2+x3+0.6x4+1.8x5≥70,0.1x1+0.05x2+0.02x3+0.2x4+0.05x5≥3,0.05x1+0.1x2+0.02x3+0.2x4+0.08x5≥10,x1≥0,x2≥0,x3≥0,x4≥0,x5≥0},{x1,x2,x3,x4,x5}]Out[11]={24.7436,{x1→0.,x2→0.,x2→0.,x4→39.7436,x5→25.641}}2、某工廠生產(chǎn)四種不同型號的產(chǎn)品，而每件產(chǎn)品的生產(chǎn)要經(jīng)過三個車間加工，根據(jù)該廠現(xiàn)有設(shè)備和勞動力等生產(chǎn)條件，可以確定各車間每日的生產(chǎn)能國（折合成有效工時數(shù)表示）。各車間每日可利用的有效工時數(shù)、每個產(chǎn)品在各車間加工時所花費的工時數(shù)以及每件產(chǎn)品可獲得的利潤見下表，問每種產(chǎn)品每季度各應(yīng)該生產(chǎn)多少，才能使這個工廠每季度生產(chǎn)總值最大？車間每件產(chǎn)品所需的加工工時有效工時（h/d）1#2#3#4#IIIIII0.80.81.11.20.60.80.70.80.40.50.70.7160120100利潤（元/件）68910解：設(shè)各生產(chǎn)件數(shù)為:x1,x2,x3,x4,即為:Maxf=6x1+8x2+9x3+10x4條件:0.8x1+0.8x2+1.1x3+1.2x4≤160*90(*一季度為90天*)0.6x1+0.8x2+0.7x3+0.8x4≤120*900.4x1+0.5x2+0.7x3+0.7x4≤100*90方法一：用NMaximizeIn[12]:=NMaximize[{6x1+8x2+9x3+10x4,0.8x1+0.8x2+1.1x3+1.2x4≤160*90,0.6x1+0.8x2+0.7x3+0.8x4≤120*90,0.4x1+0.5x2+0.7x3+0.7x4≤100*90,x1≥0,x2≥0,x3≥0,x4≥0},{x1,x2,x3,x4}]Out[12]={126000.,{x1→0.,x2→4500.,x3→0.,x4→9000.}}方法二:用LinearProgrammingIn[13]:=c={6,8,9,10}A={{0.8,0.8,1.1,1.2},{0.6,0.8,0.7,0.8},{0.4,0.5,0.7,0.7}}b={160,120,100}*90(*一季度為90天*)x0=LinearProgramming[-c,-A,-b]c.x0Out[13]={6,8,9,10}Out[14]={{0.8,0.8,1.1,1.2},{0.6,0.8,0.7,0.8},{0.4,0.5,0.7,0.7}}Out[15]={14400,10800,9000}Out[16]={0.,4500.,0.,9000.}Out[17]=126000.方法三:用ConstrainedMaxIn[18]:=ConstrainedMax[6x1+8x2+9x3+10x4,{0.8x1+0.8x2+1.1x3+1.2x4≤160*90,0.6x1+0.8x2+0.7x3+0.8x4≤120*90,0.4x1+0.5x2+0.7x3+0.7x4≤100*90},{x1,x2,x3,x4}]ConstrainedMax::deprec:ConstrainedMaxisdeprecatedandwillnotbesupportedinfutureversionsofMathematica.UseNMaximizeorMaximizeinstead.More…Out[18]={126000.,{x1→]0.,x2→4500.,x3→0.,x4→9000.}}3、使用兩個求解線性規(guī)劃問題的函數(shù)，解：方法一：用ConstrainedMinIn[19]:=Clear[x,y,z]ConstrainedMin[-3x+y+z,{x-2y+z≤11,-4x+y+2z≥3,-2x+z==1},{x,y,z}]Out[19]={-2,{x→4,y→1,z→9}}方法二:用NMinimizeIn[27]:=NMinimize[{-3x+y+z,x-2y+z≤11,-4x+y+2z≥3,-2x+z==1,x>0,y>0,z>0},{x,y,z}]Out[27]={-2.,{x→4.,y→1.,z→9.}}方法三:用LinearProgrammingIn[28]:=c={-3,1,1}A={{-1,2,-1},{-4,1,2},{-2,0,1}}b={-11,3,1}x0=LinearProgramming[c,A,b]c.x0Out[28]={-3,1,1}Out[29]={{-1,2,-1},{-4,1,2},{-2,0,1}}Out[30]={-11,3,1}Out[31]={4,1,9}Out[32]=-24、教材上自己尋找到的問題或者自己感興趣的問題。今年(2007)湖北省高考數(shù)學(xué)題(文科11題,理科13題)設(shè)變量x,y滿足約束條件,求目標函數(shù)2x+y的最小值方法一：In[33]:=NMinimize[{2x+y,x-y+3≥0,x+y≥0,x≥-2,x≤3},{x,y}]Out[33]={-1.5,{x→-1.5,y→1.5}}方法二：In[]:=x=x1-2;ConstrainedMin[2x+y,{x-y+3>=0,x+y>=0,x>=