某饲料公司生产鸡混合饲料配料

1、配料问题某饲料公司生产鸡混合饲料，每千克饲料所需营养质量要求如表C-1所示.表C-1每千克饲料所需营养质量要求营养成分肉用种鸡国家标准肉用种鸡公司标准产蛋鸡标准代谢能2.72.8Mcal/kg2.7Mcal/kg2.65Mcal/kg粗蛋白135145g/kg135145g/kg151g/kg粗纤维<50g/kg45g/kg25g/kg赖氨酸5.6g/kg5.6g/kg6.8g/kg蛋氨酸2.5g/kg2.6g/kg6g/kg钙2340g/kg30g/kg33g/kg有机磷4.66.5g/kg5g/kg3g/kg食盐3.7g/kg3.7g/kg3g/kg公司计划使用的原料有玉米、小麦、麦

2、萩、米糠、豆饼、菜子饼、鱼粉、槐叶粉、DL-蛋氨酸、骨粉、碳酸钙和食盐等12种.各原料的营养成分含量及价格见表C-2.表C-2原料的营养成分含量及价格序号原料单价元/kg代谢能Mcal/kg粗蛋白g/kg粗纤维g/kg赖氨酸g/kg蛋氨酸g/kg钙g/kg有机磷g/kg食盐g/kg1玉米0.683.3578162.31.20.70.32小麦0.723.08114223.41.70.60.343麦0.231.78142956.02.30.3104米糠0.222.10117726.52.71.0135豆饼0.372.404024924.15.13.25菜6子0.321.623601138.17.1

3、5.38.4饼7鱼粉1.542.8045029.111.86327槐8叶0.381.6117010810.62.244粉DL-9蛋氨23980酸10骨粉0.56300140碳11酸1.12400钙12食盐0.421000公司根据原料来源，还要求1吨混合饲料中原料含量为：玉米不低于400kg、小麦不低于100kg、麦萩不低于100kg、米糠不超过150kg、豆饼不超过100kg、菜子饼不低于30kg、鱼粉不低于50kg、槐叶粉不低于30kg,DL-蛋氨酸、骨粉、碳酸钙适量.(1)按照肉用种鸡公司标准，求1kg混合饲料中每种原料各配多少，成本最低，建立数学模型并求解.(2)按照肉用种鸡国家标准，求

4、1kg混合饲料中每种原料各配多少，成本最低.(3)公司采购了一批花生饼，单价是0.6元/kg,代谢能到有机磷的含量分别为(2.4,38,120,0,0.92,0.15,0.17)，求肉用种鸡成本最低的配料方案.(4)求产蛋鸡的最优饲料配方方案.(5)公司考虑到未来鱼粉、骨粉和碳酸钙将要涨价，米糠将要降价，价格变化率都是原价的5%试对两种产品配方方案进行灵敏度分析.说明：以上5个问题独立求解和分析，如在问题(3)中只加花生饼，其他方案则不加花生饼.某饲料公司生产鸡混合饲料配料优化研究作者院（系）人文管理学院专业数学与应用数学年级2011级学号实验成绩日期2014年6月19日某饲料公司生产鸡混合饲

5、料配料优化研究1问题描述某饲料公司生产鸡混合饲料，每千克饲料所需营养质量要求如表C-1所示.表C-1每千克饲料所需营养质量要求营养成分肉用种鸡国家标准肉用种鸡公司标准产蛋鸡标准代谢能2.72.8Mcal/kg2.7Mcal/kg2.65Mcal/kg粗蛋白135145g/kg135145g/kg151g/kg粗纤维<50g/kg45g/kg25g/kg赖氨酸5.6g/kg5.6g/kg6.8g/kg蛋氨酸2.5g/kg2.6g/kg6g/kg钙2340g/kg30g/kg33g/kg有机磷4.66.5g/kg5g/kg3g/kg食盐3.7g/kg3.7g/kg3g/kg公司计划使用的原料

6、有玉米、小麦、麦萩、米糠、豆饼、菜子饼、鱼粉、槐叶粉、DL-蛋氨酸、骨粉、碳酸钙和食盐等12种.各原料的营养成分含量及价格见表C-2.表C-2原料的营养成分含量及价格序号原料单价元/kg代谢能Mcal/kg粗蛋白g/kg粗纤维g/kg赖氨酸g/kg蛋氨酸g/kg钙g/kg有机磷g/kg食盐g/kg1玉米0.683.3578162.31.20.70.32小麦0.723.08114223.41.70.60.343麦萩0.231.78142956.02.30.3104米糠0.222.10117726.52.71.0135豆饼0.372.404024924.15.13.256菜子饼0.321.6236

7、01138.17.15.38.47鱼粉1.542.8045029.111.863278槐叶粉0.381.6117010810.62.2449DL-蛋氨酸2398010骨粉0.5630014011碳酸钙1.1240012食盐0.421000公司根据原料来源，还要求1吨混合饲料中原料含量为：玉米不低于400kg、小麦不低于100kg、麦萩不低于100kg、米糠不超过150kg、豆饼不超过100kg、菜子饼不低于30kg、鱼粉不低于50kg、槐叶粉不低于30kg,DL-蛋氨酸、骨粉、碳酸钙适量.(1)按照肉用种鸡公司标准，求1kg混合饲料中每种原料各配多少，成本最低，建立数学模型并求解.(2)按照肉

8、用种鸡国家标准，求1kg混合饲料中每种原料各配多少，成本最低.(3)公司采购了一批花生饼，单价是0.6元/kg,代谢能到有机磷的含量分别为(2.4,38,120,0,0.92,0.15,0.17)，求肉用种鸡成本最低的配料方案.(4)求产蛋鸡的最优饲料配方方案.(5)公司考虑到未来鱼粉、骨粉和碳酸钙将要涨价，米糠将要降价，价格变化率都是原价的，试对两种产品配方方案进行灵敏度分析.2建模分析设公司计划使用的原料有玉米、小麦、麦萩、米糠、豆饼、菜子饼、鱼粉、槐叶粉、DL-蛋氨酸、骨粉、碳酸钙和食盐的用量分别为Xj,j1,2,12,若将相应的原料单价分别用Cj,j1,2,12,来表示，则其总成本可以

9、用下面的线性函数来表示即6zCjXj.j12.1 问题（1）模型根据问题（1）所给数据及问题要求可列出约束条件，所以可建立混合饲料配料计划的数学模型如下：minz0.68x10.72X20.23x30.22x40.37x50.32x61.54x70.38凡23X90.56x101.12x110.42x123.35x13.08x21.78x32.10x42.40x51.62x62.80x71.61x82.73.35x13.08x21.78x32.10x42.40x51.62x62.80x71.61x813578x1114x2142x3117x4402x5360x6450x7170x814516x

10、122x295x372x449x5113x6108x8452.3x13.4x26.0x36.5x424.1x58.1x629.1x710.6x85.61.2x11.7x22.3x32.7x45.1x57.1x611.8x72.2x8980x92.60.7x10.6x20.3x31.0x43.2x55.3x663x74x8300x10400x11300.3x10.34x210x313x45x58.4x627x74x8140x1051000x123.7Xx2x3刈x5x6x7xx9X。刈为21x10.4,x20.1,x30.1x40.15x50.1x0.03x0.05x0.03xj0,（j1,2,

11、.,12）根据问题（2）所给数据及问题要求可列出约束条件，所以可建立混合饲料配料计划的数学模型如下:minz0.68x10.72x20.23x30.22x40.37x50.32x61.54x70.38x823x90.56x101.12x110.42x123.35xi3.08x21.78x32.10x42.40x51.62%2.80x71.61x82.73.35x13.08x21.78x32.10x42.40x51.62x62.80x71.61x82.878x1114x2142x3117x4402x5360x6450x7170x813578x1114x216x122x2142x395x3117x

12、4402x5360x6450x7170x814572x449x5113x6108x8502.3x13.4x26.0x36.5x424.1x58.1x629.1x710.6x85.61.2x11.7x22.3x32.7x45.1x57.1x611.8x72.2x8980x92.50.7x10.6x20.3x31.0x43.2x55.3x663x74x8300x10400x11200.7x10.6x20.3x31.0x43.2x55.3x663x74x8300x10400x11400.3x10.34x210x313x45x58.4x627x74x8140x104.60.3x10.34x210x31

13、000x123.7为x2x3x4x513x4x6x5x58.4x627x74x8140x106.57x8x9x10x11x)21x10.4x20.1x30.1x40.15x50.1%0.03x0.05x0.03xj0,j1,2,.,12根据问题（3）所给数据及问题要求按照肉用种鸡公司标准可列出约束条件，所以minz0.68x10.72x2O23x30.22x40.37x50.32x61.54x70.38x823x90.56xi01.12xii0.42肌0.6刈3.35xi3.08x21.78x32.10x42.40x51.62x62.80x71.61x82.4x132.778xi114x214

14、2x3117x4402k360x6450x7170x838x1313578x1114x2142x3117x4402x5360刈450x7170凡38x1314516xi22x295x372x449%113%108x8120x13452.3xi3.4x26.0x36.5x424.1x58.1x629.1x710.6x85.61.2xi1.7x22.3x32.7x45.1x57.1x611.8x72.2x8980x90.92。2.60.7xi0.6x20.3x31.0x43.2x55.3x663x4x8300为。400刈0.15x13300.3xi0.34x210x313x45x58.4x627x

15、74x8140xi00.17x1351000xi23.7xix2x3x4x5x6xx8x940刈刈刈1xi0.4x20.1x30.1x40.15x50.1x60.03x70.05x80.03xj0,j1,2,.,13根据问题（3）所给数据及问题要求按照肉用种鸡国家标准可列出约束条件，所以可建立混合饲料配料计划的数学模型如下：minz0.68x10.72x20.23x30.22x40.37x50.32x61.54x70.38x823x90.56x101.12x110.42x120.6x133.35xi3.08x21.78x32.10x42.40x51.62x62.80x71.61x82.4x13

16、2.73.35x13.08x21.78x32.10x42.40x51.62x62.80x71.61x82.4x132.878x1114x2142x3117x4402x5360x6450x7170x838x1313578x1114x2142x3117x4402x5360x6450x7170x838x1314516x122x295x372x449x5113x6108x8120x13502.3x13.4x26.0x36.5x424.1x58.1x629.1x710.6x851.2x11.7x22.3x32.7x45.1x57.1x611.8x72.2x8980x90.92x132.50.7x10.6

17、x20.3x31.0x43.2x55.3x663x74x8300x10400x110.15x13200.7x10.6x20.3x31.0x43.2x55.3x663x74x8300x10400x110.15x13400.3x10.34x210x313x45x58.4x627x74x8140x100.17x130.3x10.34x210x313x45x58.4x627x74x8140x100.17x136.51000x123.7x1x2x3x4x5x6x7x8x9x10x11x12x131x10.4x20.1x30.1x40.15x50.1x60.03x70.05x80.03xj0,j1,2,.

18、,13根据问题（4）所给数据及问题要求产蛋鸡的标准可列出约束条件，所以可建立混合饲料配料计划的数学模型如下；minz0.68x10.72x20.23x30.22x40.37x50.32x61.54x70.38x823x90.56x101.12x110.42x123.35xi3.08x21.78x32.10x42.40x51.62x62.80x71.61x82.78x1 114 x216x1142x3117x4402x5360x6450x7170x815122x295x372x449x5113x6108x8252.3x13.4x26.0x36.5x424.1x58.1x629.1x710.6x8

19、6.81.2x1 1.7x2 2.3x3 2.7x4 5.1x50.7x1 0.6x20.3x3 1.0x4 3.2x57.1x6 11.8x7 2.2x8 980x9 65.3x663x7 4x8 300x10 400x11330.3x1 0.34x210x313x45x58.4x627x74x8140x1031000x123x1x2x3x4x5x6x7x8*9x1°x11x121x10.4x20.1x30.1x40.15x50.1x60.03x70.05x80.03xj0,j1,2,.,123程序设计3.1 问题（1）的程序用WinQSB对问题（1）求解的程序如图3.1.Vari

20、abkXI凌X?乂4X5XGX?xa乂9XI0X11X12hrechorr.n.MinaiiMi068720.230.22O.370.321.5+0.38230.561.120.42Cl3353082.102.401.G22.8。1.61>=2,7C278114T4211740236045。T70>-135C37B114142(17402360450170<-1亘C41£229572491t310S<-45C52.3J.46.0G.524.18.129.110.6>=E6LB1.21.72.32.15.!7.1ll.S2.2>=2.bC7n7nEn

21、3in3253SS43on4P030CB0.3034101358.4274140>=5LU1UUU3.Z111t1111t111sLowerBi00.40.00U130.05000000UpperBiMMMa.is0.1MMMMMMV3riablEitinuDut-btiniiuou-Btfiinuou«itinuokivllinuiDurrktiniiowliinuautfttiruoijifbtinuou*itinwuitifinuputLliniuout图3.1问题（1）的程序3.2 问题（2）的程序用WinQSB对问题（2）求解的程序如图3.2.Vaiiabl对X2X3

22、x+X5XG乂7X8X9XI0X11XI2hrectioiR.H.MinimizO.GS0l720.230.220.370.321.542.30.5G1.12a.42C13.353.OS1-Tfi2.102,401.622.80161>=2.7C23.353.OS1.782.102.40L622.801.CT2.878in142117402痴伽170>=135C478in142117402360450170<=U5C51&22957249113ioe50CG2.33.46.06.524.1S.129.110.G>=5.6C7121.72.32.75.17.111

23、.82.2980>=2.5匚80.7O.EC.31.03.25.3£343GQ400>=20C90.70.60.3ID3.25.36.34300400<=40CIO0.30.34101358.4274140A三4£C110.30,1013584274140<=&5Cl2woo,3.7Cl3111111111111s1LoweiB0.40.10.1000.03D.050.030000LIpperBMMMU.15U.1MMMMMMMVariablitinuoustinuoutinuoustinLioostinuaustinuoustinuoust

24、inuous：tinuoostinuaus：tinuaustinuous图3.2问题（2）的程序3.3 问题（3）的程序用WinQSB对问题（3）按照肉用种鸡公司标准求解的程序如图3.3（a）VanablXIX2N?刈X5X£乂7X8X9XI0|XIIXI2XI3iirectioR.H.Minimi;0.G8fl720.230.220L370.321-54(L38231.120.4?OlGf?13.353.0flT.782J241.522S1.61Q0002.4>=2.7C2匚沟142117402360*5017000003B>-135C3761141421174023G

25、0450170000038<=145C416229572491131000an0120<=45C52.3346E5241e.i29.11Q.B00000>=5.6CG1.21.72.32.75.17.111.82.2S800000.92>-2.6C70.70.G0.313.25.3£34030040000.15>=30LS0.30.3410135S.4274014Q0a0.17>=5C30o000G0a001000037CIO1111111111i111LowerEn.40.10.1000.030.050.0300000Upper!MMM0L150

26、.1MMMMMMMMVariabliniiou筝inuou$inuQU/ilDUOUfiinuouTinuoutinuoutinuou#inuQginuousinuQusimjousinuous图3.3（a）问题（3）的程序用WinQSB对问题（3）按照肉用种鸡国家标准求解的程序如图3.3（b）VaiiablXIxzX3X4X5XGX7X8xsXI0X11X12X13'ireclioifl.w.Minimisa.720.2322fl.37Q.321.540.38230.5G1.120.420.6C13.353.DBL782,12.41.622,81.6100002.42.7C23.35

27、3.C81.7B2.12.4T.622.816100002.4<=28C378114142117402制*5。170000038>-135C4781141421174023G045017000Q030<=145C51G229572491131D8000120!=:5DCG2,334G6.524.18.129,110.G0000>-5而C71.2M2.32.75.17.1T1.82.29B00000.922.5C80.70«0.313.25.3834030040Q00.1523匚90.70G0.313.25.3G34030040000.15<=40CID0

28、.30.34ID135S.42740140000.17=4.6匚110.30.34101350,42740140000.17<=E5C1200000000000100037£131111111I11111a1LowerE0.40.10-1000.030.050.03Q0000UpperEMMM150.1MMMMMMMMVsriabliniousinuQU善inuQginuQU*inuoufinuourinuouTimuourinuoutinuw事inuousihuousinuous图3.3（b）问题（3）的程序3.4 问题（4）的程序VariablXIX2X3X4ZbXGX7X

29、9X9XI0XHXt2iirectiE)R.H.Minimi:0,8n,720.2322370.321.540.3823D.5K1J2P4ZC13.353.A81.782.102401.S22.801.1>-2.65C278114142(17402360450170151C3IB2235124g113108<=25C*2.36.06.524.10129.11DG>-S.8£51.21.7232.7517.111.8Z2960G£6370.603103,25,3634300400>-33C70.30.34101358.4274140>=3C8IO

30、DO=5C911111111111.1Lowcrl040.10.1000.030.050.030000Upper!MMM0.1501MMMMMMVariablinuousinuousinuousinuousinuousinuousinuousinuousimiousimuouMinuousinuou图3.4问题（4）的程序4结果分析4.1 问题（1）的结果分析问题（1）的求解结果如图4.1:1G：0&362010-4-20f2010-4-20?D1Q-4-20|2OlO-4-2D|：DecisionSolulionUnitCostIotalReducedAllowableAllowab

31、e1乂1r()L275g:O.GQOO0.187C0basic0LGG54OSIDO2H4QOO0.72000.2890OJ465atbound0.5735M3X300.230000.2301atbound-0.0001M4X40.04060.2200D01070basicO_157fl02702忌乂5Ol05470.3700002020basic-0.86390.40036XGOlASDO0.32000.0D9GQ.O51Eatbound0.2GS4M7X70LC7S31.54000.117400L93201,76卯9xa0.03000.3M00.D114fl_477«atboun

32、d-o.razeM9X9Q23.0000023.9568atbound-0.95&0M1C乂10Q.CS090.56000.04530b-asic-0.78430.601811X1101.12000&G544mtbound1.0656M12X120.00370.42000.00160bsicMMObjecti¥«Function(Min.)=&G918LeftRighlSlackShadowAllowableallowabletC12.7000>=之7000fl0.47022.563727G53ZC2145.0000>=135,0000I

33、QOOQDDM145.00(103C3145.0000145.000900.0003135.000015388674C426.021345.0000IS.97870260213M5C56.4Q81>=5.6OD0C.&0810M6.40B16C5>=Z.600D00.1Q8Q2.40802,30077C730.0000>=30.0000o0051190393注5554S匚H14.87&0>-5.00003.87600M14.87609C93.7000=3700000001402221801CC10Lfl口口口1HOOD0-0.95E8(L9B1S1,03

34、8Z图4.1问题（1）求解结果按照肉用种鸡公司标准，求1kg混合饲料中使用的原料有玉米、小麦、麦萩、米糠、豆饼、菜子饼、鱼粉、槐叶粉、DL-蛋氨酸、骨粉、碳酸钙和食盐的用量分别为0.275kg,0.4kg,0kg,0.0486kg,0.0547kg,0.03kgO0763kg,0.03kg,0kg,0.0809kg,0kg,0.0037kg,成本最低为0.6918元.4.2 问题（2）的结果分析问题（2）的求解结果如图4.2:1C:17:0120146172014-G-1?2O14-t-172014-G-12)eci$iqnSolutionUnitCottTotalReducedBasifAl

35、lowableMlowable1XID.50070.6»000.34050baiK0.Z87575122X20.100007200DO7200.1352atbound05848M3X30.10000.23000.0230D.12&0扯boimd0.1040M4X40.Q7770.22000.01710b-asic0.DB190.24245X50.05立0.370口00210Dbasic口353。OrGE136X&D.03DO0.32000.009G0.2252atbound0.0948M7X7D05001.54000.07701.011Satbound0.5284M8

36、X8D.0300038000.01140.315Dstbound0.0650M3X90.00D123000a00030basic-0.53898.35591(XI0001640.5E000.00920b曰工ic0.07940.693D11XII0.03441.12000.D38C0baiic0.34271.643112X1200037042皿oooie0basic制M0b|ecliveFumchcmi|M>n1=D.G213LeftRiahtSlackShadowAllowableAllowable1C127000>=2.700000.3E402.B2382.78192C22.70

37、00<=2.80000.100D02.7000M3C3135.0000>-135.000000.00011289460145.00004C4135.0000<=145.000010.00DO0135.0000M5C534.7226«=50.00001527740347226M6C&5.9827?=5.60000.39270M5.98277C72.5000>=2.5000000292,370124.96229C920.000020.000000.004211472729.1G829C920.000040.000020.0000020.0000M10CIO

38、6.500D>=4.EOOO1.9QDQM£.500011C11G500D<=6.50000-D.0D104.60DO12.499512C123.7000=3.700I0000010026.620613Cl3roooo1.00000054990.97711.0213图4.2问题（2）求解结果按照肉用种鸡国家标准，求1kg混合饲料中使用的原料有玉米、小麦、麦萩、米糠、豆饼、菜子饼、鱼粉、槐叶粉、DL-蛋氨酸、骨粉、碳酸钙和食盐的用量分别为0.5007kg,0.1kg,0.1kg,0.0777kg,0.0568kg,0.03kg,0.05kg,0.03kg,0.0001kg,

39、0.0164kg,0.0344kg,0.0037kg,成本最低为0.6213元.4.3 问题(3)的结果分析用WinQSB对问题（3）按照肉用种鸡公司标准求解的结果如图3.3（a）10:13:40Thui&dapApril22-2010|1DechionVariableSolutionValueUnitCostarProfitcj)TotalConiributionReducedCastBasisStatusAllowableMin.c(j)AllowableMx.cj1XI0,5305300口3662Qbaic-0.32530.79302X2QJOOO0.72000.07200.16

40、07albound0.5593MX30.1»。&0口0.023003295athound0.0995MX4a0.220000.14ISalboundD.0754MX60.07210.37000.02G70basic0.2S<JU0.G9S56X6X71)03000.3200000960.3053atbound0141M70.09001.54000.07700.4502atbound1.083BMxeD.03DaQ.3SOD0.Q114口5435atbmund0L1G35MgX9Q.000323.00000.Q074Qbosic-1.1200+1.714110X10D.0

41、4260.56000239flbasic0.13200.G343XII0C3271.1200003G60basic1.0201L542312XI2O.AOJ?(M2U00.001G0basicMM13X13a0.600000,4351atboundD.1649MObiecti'weFunctionMin=0G554ContnintLeftHandSideDirectionRightHandSideSlackorSurplusShadowPriceAllowableMin.HHSAllowableMe巩RHS1Cl2.7000>=2700000,52132.6610Z.72712C2135.00001.000000.0002129.8679144.64593C3135.0000<=145.0000惟OOM0135.0000M4C430.4805<=45.000014.5195030.4905M5C55.S329>=5.GOOD0.2329DM5.9329CCGZeODQ>=2.600000.024CN28311003307C730.000030.000000.00562