求解二次規(guī)劃問題

32求解二次規(guī)劃問題LINDO可以求解二次規(guī)劃〔QP〕問題。例如：minf3x2y2xy0.4y1.2x0.9y1.1s.t.xy1y0.7LAGRANGE乘子法，得2y2xy0.4yA1.2x0.9y1.1Bxy1Cy0.7，x、y求偏導(dǎo)，得到兩個(gè)約束條件：6xy1.2AB00.9ABC0.4LINDO中輸入以下命令：MINX+Y+A+B+CST6X-Y-1.2A+B>02Y-X-0.9A+B+C>-0.41.2X+0.9Y>1.1X+Y=1Y<0.7END注釋 ：MINX+Y+A+B+C一句只代表變量的出場挨次；QCP445行開頭。LINDO運(yùn)行后輸出以下結(jié)果：STATUSOPTIMALQPOPTIMUMFOUNDATSTEP 7OBJECTIVEFUNCTIONVALUE1) 1.355556VARIABLEVALUEREDUCEDCOSTX0.6666670.000000Y0.3333330.000000A10.8888890.000000B9.4000000.000000C0.0000000.366667ROW SLACKORSURPLUS DUALPRICES2) 0.000000-0.6666673) 0.000000-0.3333334) 0.000000-10.8888895) 0.0000009.4000006) 0.3666670.000000NO.ITERATIONS= 7這個(gè)結(jié)果說明：LINDO求解此二次規(guī)劃問題〔QP〕共用7步迭代得到最優(yōu)fmin=1.355556X=0.66666Y=0.3333350.366667，04問題的最優(yōu)解〔影子價(jià)格〕DUALPRICES為Y1=-0.666667，Y2=-0.333333，Y3=-10.888889，Y4=9.4，Y5=0。農(nóng)戶生產(chǎn)的優(yōu)化模型候狀況之上。假設(shè)〔面積單位：畝：1X=用于完成上繳國家任務(wù)的小麥一年總種植面積1234X=用于生產(chǎn)、生活的小麥一年總種植面積X=用于生產(chǎn)、生活的油菜一年總種植面積X=用于生產(chǎn)、生活的紅薯一年總種植面積23456X=用于完成上繳國家任務(wù)的棉花一年總種植面積X=用于生產(chǎn)、生活的棉花一年總種植面積5678X=用于完成上繳國家任務(wù)的玉米一年總種植面積X=用于生產(chǎn)、生活的玉米一年總種植面積789X=用于生產(chǎn)、生活的芝麻一年總種植面積9X =用于生產(chǎn)、生活的花生一年總種植面積1011X=用于生產(chǎn)、生活的大豆一年總種植面積111213141516X=用于生產(chǎn)、生活的西瓜一年總種植面積X=用于生產(chǎn)、生活的番茄一年總種植面積X=用于生產(chǎn)、生活的白菜一年總種植面積X=用于生產(chǎn)、生活的辣椒一年總種植面積X=用于生產(chǎn)、生活的茄子一年總種植面積1213141516X17=用于生產(chǎn)、生活的豆角一年總種植面積X18=用于生產(chǎn)、生活的蘿卜一年總種植面積F(1，X2。18該農(nóng)戶一年總的純收入該農(nóng)戶家庭人口6人，無剩余勞動(dòng)力，共有可耕地12畝。生產(chǎn)細(xì)節(jié)如下表：播種時(shí)間收獲時(shí)間生長期〔天〕打算種植/年〕畝產(chǎn)量〔斤/畝〕家庭上〔斤/年〕每畝投資〔元〕小麥9月中旬4月2401060078075油菜9月中旬4月2301.520050紅薯5月中旬9月下旬1353.0202380棉花4月下旬9月下旬1603.010030080玉米5月中旬9月下旬904.070060036芝麻5月中旬9月上旬1000.512020花生5月上旬8月下旬1100.230040大豆5月中旬8月下旬901.015010西瓜5月上旬8月中旬901.03500100番茄4月下旬9月中旬1400.110000120白菜4月下旬9月下旬900.110000120辣椒4月中旬10月上旬1800.1(干)20090茄子4月中旬10月上旬1800.0510000100豆角4月下旬9月下旬1400.056250120蘿卜6月中旬10月上旬1100.91000050國家收購價(jià)市場價(jià)〔元/必需口糧數(shù)喂養(yǎng)家畜消果籽出油率植物油需求〔元/斤〕斤〕〔斤/年〕〔斤/年〕〔a%/畝〕量〔斤/年〕小麥0.320.354380油菜1.0015%30紅薯0.196001500棉花2.9510%12玉米0.220.272600芝麻2.0040%6花生0.90大豆0.90西瓜0.12番茄0.08白菜0.05辣椒5.00茄子0.06豆角0.20蘿卜0.05依據(jù)上表狀況，得到：12，

利潤0.35〔600X1

-780〕+0.32*780-75X1

=135X

-30；10.35〔600X2

-4380〕-75X323

=135X2

-1533；200X3

≥30，利潤200X3

–30–50X

；=150X414

-30；紅薯：2023X ≥600+1500，利潤0.19〔2023X4

–2100〕–80X

=300X4

-399；100X5

≥300，10%*100X6

≥12，2.95*100X

-80X-80X=215X-80X ；5 5 6 5 6700X7

≥600，700X8

≥2600，利潤0.27〔700X7

-600〕+0.22*600-36X7

=153X7

–30,0.27〔700X-600〕-36X8

=153X8

–702,40%*120X9

≥6，2〔120X9

-6/0.4〕-20X9

=220X9

-30；0.90*300X100.90*150X11

-20X10-10X11

=250X；10=125X；110.12*3500X12

-100X12

=320X；120.08*10000X130.05*10000X14

-120X13-120X14

=680X；13=380X；145*200X15

-90X15

=910X；120.06*10000X16

-100X16

=500X；120.20*6250X17

-120X17

=1130X；170.05*10000X18

-50X18

=450X；18得到模型如下：maxf135x1135x2150x3300x4215x580x6153x7153x8220x9250x10125x11320x121130x17450x182023.460x178,60x2438,20x33,20x421,x53,10x612, 6 26 1

,x87

,x97

,x1x2x312,818

12,xj0LINDO中送入以下命令：MAX135X1+135X2+150X3+300X4+215X5-80X6+153X7+153X8+220X9+250X10+125X11+320X12+680X13+380X14+910X15+500X16+1130X17+450X18ST60X1>7860X2>43820X3>320X4>21X5>3X6<1.27X7>67X8>268X9<1X1+X2+X3=12X4+X5+X6+X7+X8+X9+X10+X11+X12+X13+X14+X15+X16+X17+X18=12END得到結(jié)果：LPOPTIMUMFOUNDATSTEP 81) 7148.214VARIABLEVALUEREDUCEDCOSTX11.3000000.000000X27.3000000.000000X33.4000000.000000X41.0500000.000000X53.0000000.000000X60.0000001210.000000X70.8571430.000000X83.7142860.000000X90.000000910.000000X100.000000880.000000X110.0000001005.000000X120.000000810.000000X130.000000450.000000X140.000000750.000000X150.000000220.000000X160.000000630.000000X173.3785720.000000X180.000000680.000000ROW SLACKORSURPLUS DUALPRICES2) 0.000000-0.2500003) 0.000000-0.2500004) 65.0000000.0000005) 0.000000-41.5000006) 0.000000-915.0000007) 1.2023000.0000008) 0.000000-139.5714269) 0.000000-139.57142610) 1.0000000.00000011) 0.000000150.00000012) 0.0000001130.000000NO.ITERATIONS= 8RANGESINWHICHTHEBASISISUNCHANGED:OBJCOEFFICIENTRANGESVARIABLEALLOWABLECOEFCURRENTINCREASEALLOWABLEDECREASEX1135.00000014.999999INFINITYX2135.00000014.999999INFINITYX3150.000000INFINITY14.999999X4300.000000830.000000INFINITYX5215.000000915.000000INFINITYX6-80.0000001210.000000INFINITYX7153.000000976.999939INFINITYX8153.000000976.999939INFINITYX9220.000000910.000000INFINITYX10250.000000880.000000INFINITYX11125.0000001005.000000INFINITYX12320.000000810.000000INFINITYX13680.000000450.000000INFINITYX14380.000000750.000000INFINITYX15910.000000220.000000INFINITYX16500.000000630.000000INFINITYX171130.000000INFINITY220.000000X18450.000000680.000000INFINITYRIGHTHANDSIDERANGESROWALLOWABLERHSCURRENTINCREASEALLOWABLEDECREASE278.000000195.00000077.9999923438.000000195.000000438.00000043.00000065.000000INF