1、农场生产计划-数学建模农场生产计划 数学模型问题重述 某农场有3万亩农田,欲种植玉米、大豆和小麦三种农作物各种作物每亩 需施化肥分别为012吨、020吨、0.15吨预计秋后玉米每亩可收获500千克, 售价为024元千克,大豆每亩可收获200千克,售价为120元千克,小麦每亩可收获350千克,售 价为070元/千克农场年初规划时考虑如下几个方面:第一目标:年终收益不低于350万元;第二目标:总产量不低于125万吨;第三目标:玉米产量不超过06万吨,大豆产量不少于02万吨,小麦产量以 05万吨为宜,同时根据三种农作物的售价分配权重;第四目标:农场现能提供5000吨化肥;若不够,可在市场高价购买,但希 望高价采购量愈少愈好.模型假设与建立模型假设:1、假设农作物的收成不会受天灾的影响2、假设农作物不受市场影响,价格既定用x ,x ,x分别表示用于种植玉米、大豆、小麦的农田(单位:亩)123mm z = pi整理数据列表如下所示:物种玉米大豆小麦亩产量(千克)500200350售价(元/千克)0.241.20.7售价(元/亩)100240245施肥量(亩/吨)0.120.20.15变量设置(亩
2、)x1x2x3* d _ + p * d _ + p (旦* d -+ -60* d - + 竺* d - + 竺 d +) + p * d +1223 107310741075107 5 S 6模型建立约束条件(1)刚性约束x + x + x = 300001232)柔性约束 第一目标:年终收益不低于350万元;min d -丿120x + 240x + 245x + d - - d + = 350000012311第二目标:总产量不低于十25万吨;I min d -丿-d + 二125000002500x + 200x + 350x + d -第三目标:玉米产量不超过06万吨,大豆产量不少于02万吨,小麦产量 以0.5万吨为宜,iJ min 乞 + 了 500x + d V13mm d -丿4200 x + dJ24-d + 二 60000003V1232d + = 2000000 4min-+ d +丿55135x + d - - d + = 5000000V 255第四目标:农场现能提供5000吨化肥;若不够,可在市场高价购买,但希 望高价采购量愈少愈好.I min d + 丿
3、10.12x + 0.2x + 0.15x + d 一一 d + = 5000000V12366模型求解:(见附件)种植面积:玉米:5915.714亩土豆:9798.571亩小麦:14285.71亩能够得到一个满足条件的种植计划 附件:model: sets:L/1.4/:p,z,goal;V/1.3/:x;HN/1.1/:b;SN/1.6/:g,dp,dm;HC(HN,V):a;SC(SN,V):c;Obj(L,SN):wp,wm;endsetsdata:p=?;goal=?0;b=30000;g=3500000 12500000 6000000 2000000 5000000 5000000;a=1,1,1;c=120 240 245500 200 350500 0 00 200 00 0 350120 200 150;wp=000000000000000.24 I0 0.7 0000001;wm=1000000100000001.20.7 0000000;enddatamin=sum(L(i):p(i)*z(i);for (L(i):z(i)=sum(SN(j):wp(i,j)*
4、dp(j)+wm(i,j)*dm(j); for(HN(i):sum(V(j):a(i,j)*x(j)V=b(i);for(SN(i):sum(V(j):c(i,j)*x(j)+dm(i)-dp(i)=g(i);for(L(i)|i#lt#size(L):bnd(0,z(i),goal(i);No feasible solution found.Total solver iterations:VariableP( 1)P( 2)P( 3)P( 4)Z( 1)Z( 2)Z( 3)Z( 4) GOAL( 1) GOAL( 2)10ValueReduced Cost0.0000000.0000000.0000000.0000000.0000000.0000001.0000000.0000000.0000000.0000000.000000-0.1250000E+092417143.-3125000.0.0000000.0000000.0000000.0000000.0000000.000000GOAL( 3)GOAL( 4)X(1)X(2)X(3)B(1)G(1)G(2)G(3)G(4)G(
5、5)G(6)DP(1)DP(2)DP(3)DP(4)DP(5)DP(6)DM(1)DM(2)DM(3)DM(4)DM(5)DM(6)A(1,1)A(1,2)A(1,3)C(1,1)C(1,2)C(1,3)C(2,1)C(2,2)C(2,3)C(3,1)C(3,2)C(3,3)C(4,1)C(4,2)C(4,3)C(5,1)C(5,2)C(5,3)C(6,1)C(6,2)2417143.0.0000005915.7149798.57114285.7130000.003500000.0.1250000E+086000000.2000000.5000000.5000000.3061543.-2582429.0.0000000.0000000.0000000.0000000.0000000.0000003042143.40285.720.000000187542.91.0000001.0000001.000000120.0000240.0000245.0000500.0000200.0000350.0000500.00000.0000000.0000000.000000200.00000.00
6、00000.0000000.000000350.0000120.0000200.00000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.1250000E+090.3750000E+080.1875000E+090.1629464E+091.0000000.0000000.0000000.0000000.0000000.5580357E+080.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000C(6,3)150.00000.000000WP(1,1)0.0000000.000000WP(1,2)0.0000000.000000WP(1,3)0.00
7、00000.000000WP(1,4)0.0000000.000000WP(1,5)0.0000000.000000WP(1,6)0.0000000.000000WP(2,1)0.0000000.000000WP(2,2)0.0000000.000000WP(2,3)0.0000000.000000WP(2,4)0.0000000.000000WP(2,5)0.0000000.000000WP(2,6)0.0000000.000000WP(3,1)0.0000000.000000WP(3,2)0.0000000.000000WP(3,3)12.000000.000000WP(3,4)0.0000000.000000WP(3,5)35.000000.000000WP(3,6)0.0000000.000000WP(4,1)0.0000000.000000WP(4,2)0.0000000.000000WP(4,3)0.0000000.000000WP(4,4)0.0000000.000000WP(4,5)0.0000000.000000WP(4,6)1.0000000.000000WM(1,1)1.0000000.000000WM(1,2)0.0000000.000000WM(1,3)0.0000000.000000WM(1,4)0.0000000.000000WM(1,5)0.0000000.000000WM(1,6)0.0000000.000000WM(2,1)0.0000000.000000WM(2,2)1.0000000.000000WM(2,3)0.0000000.000000WM(2,4)0.0000000.000000WM(2,5)0.0000000.00
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