企业的营销管理问题-毕业论文

PAGEPAGE29企业的营销管理问题（物理系：段文瑞数学系：张晔韩莹）摘要本文属于企业的营销管理优化问题，主要解决的是公司最大利润、营销部的最大收入等问题。通过对影响公司利润，营销部收入的因素如公司的生产成本、宣传费用、意向订单、客户资料等的分析以及对问题的整体把握，由于最大生产能力的制约，我们需要在满足已签约的销售合同的基础上，对意向签约量有选择的安排生产，使公司的利润达到最大，而营销部应尽力争取与意向客户的签订合同，争取多销售产品时，可使总收入极大化。我们先假设在理想情况下即客户意向为100%情况下求解出方案，然后一一考虑不同客户的意向需求量，根据不同商家的期望值，及产品的不同利润有选择的进行生产。本问题中我们使用非线性规划求最优解的方法并利用MATLAB和LinGo软件进行求解。得出问题（1）中公司的利润最大为1209.685元；问题（2）营销部总收入极大为405.9621元；问题（3）兼顾公司和营销部二者的利益为元；问题（4）兼顾公司、营销部的利益以及客户的需求，尽量做到均衡销售时的利润最大为元；问题（4）使营销部总收入最大的定价、生产及销售关键字利润非线性规划最优解拟合问题重述任何一个企业都面临着将产品推向市场，销售出去。一般的，企业下设营销部，通过营销部对企业生产的产品进行销售。由于企业生产能力的制约，需要在满足已签约的销售合同量的基础上，对意向签约量有选择的安排生产。一方面，企业会组织安排生产，完成已签约的销售合同；另一方面，企业希望营销部门尽力争取与意向签约的客户签订正式销售合同；除此之外，企业还希望营销部门努力再多销售一些产品（计划外）。对于所签约的销售合同和意向签约量（计划内），企业根据销售量向营销部发放经费（包括工资以及宣传费用等）；对于计划外销售的产品，实行承包制，营销部向企业缴纳利润。产品的生产费用由企业承担，与销售有关的费用（如产品的宣传费用等）由营销部承担。宏宇电器公司2011年计划生产三类10种小家电，其中包括：热水壶（1.5升，1.8升，2升）、豆浆机（0.9升，1.1升，1.3升）、电饭煲（2升三类小家电的年最大生产能力分别为：热水壶：5万个；豆浆机：6.5万个；电饭煲6.2万个。相关的各类数据见附录一（表1至表14）分别按以下要求为宏宇电器公司制定相应的生产、销售方案：（1）使公司的利润达到最大；（2）使营销部的总收入极大化；（3）兼顾公司和营销部二者的利益；（4）兼顾公司、营销部的利益以及客户的需求，尽量做到均衡销售；（5）公司为了调动营销部的积极性，为公司多创利润，规定对于计划外销售的产品，营销部可以自行定价。统计数据显示，自行定价后每单位产品的销售价格上涨或下降5％，则三类小家电的可能销售量相应的减少或增加10％。试确定使营销部总收入最大的定价、生产及销售方案。问题分析问题（1）（2）中要求根据给出的相关数据建立模型求出最佳的生产、销售方案，分别使公司的利润达到最大和营销部的总收入极大化。通过对表分析，我们知道产品在计划内销售时带给公司的利润要大于将其在计划外销售所带来的利润益，那么必然要使计划内的订单订购量足够大（但不能超出最大生产能力），我们假设按订单的最大意向签约量签约有签约意向的客户，此时计划内的订够量最大。对于问题（3）在兼顾公司和营销部二者的利益时，把两者看作一个整体建立模型求出最佳的生产、销售方案，那么此时就不用考虑营销部给公司上缴的那一部分利润，只考虑销售的总利润以及宣传费用问题（4）当兼顾公司、营销部的利益以及客户的需求时，需要考虑顾客的要求，即要求客户的需求概率，这里用数学期望来解决问题（5）产品的销量与产品单价有一定的关系，故提高或降低价格会减少或增加销量，利用MATLAB求出目标函数的最优解，即营销部的最大总收入，同时求出每种产品价格上涨率的具体值，从而确定营销部的定价方案。模型假设（1）假设客户的订购量就是生产量，生产量就是销售量；（2）与销售有关的经费只考虑宣传费用，其他费用不考虑；（3）营销部除了只给企业上缴利润和承担宣传费用外，无其他费用支出；（4）假设问题（1）（2）（3）中，将意向客户的需求概率设为100%；（5）该企业周围的各种因素都是稳定的符号说明xi第i种产品的总销售量i=1，2···10yi计划外第i种产品的销售量i=1，2···10zi第i中产品的已签约量i=1，2···10pi第i中产品的意向签约量i=1，2···10ki第i种产品可能签订订购合同的最大合同量；i=1，2···10Qi(xi)第i种产品的宣传费函数i=1，2···10Si(xi)第i种产品的销售额函数i=1，2···10Ui第i种产品的的需求期望i=1，2···10Mi（yi）计划外第i中产品的销售额i=1，2···10Ti(yi)计划外第i种产品的上缴利润函数i=1，2···10Fi(xi)第i种产品的成本函数i=1，2···10Si(xi-yi)计划内第i种产品的销售额函数i=1，2···10Fi(xi-yi)计划内第i种产品的成本函数i=1，2···10Ni(xi-yi)计划内第i种产品的销售部经费函数i=1，2···10Hi（yi(1-0.1S)）计划外的第i种产品价格改变后的销售额函数i=1，2···10Bi（yi(1-0.1S)）价格改变后的第i种产品的上缴利润函数i=1，2···10模型的建立与求解（一）问题（1）我们可以知道公司利润就是计划内的利润和计划外的利润之和，那公司的赢利可以表示为：公司利润＝计划内销售额+计划外上缴利润－计划内成本－计划外营销部经费我们分别分析每种产品产量与成本关系表（表2），每种小家电的销售额随订购量变化(表4），计划外销售部分营销部向企业缴纳利润表(表14);用Matlab软件（运用三次拟合）编写程序，可以得出第i种产品的销售额函数Si(xi-yi)；计划外第i种产品的上缴利润函数Ti(yi)；计划内第i种产品的成本函数Fi(xi-yi)；计划外销售部经费函数Ni(yi)根据述各种准备可建立目标函数M1=约束条件（1）因为各种产品的生产量不能超过其最大生产能力，所以可得:热水壶：x1+x2+x3<=50豆浆机：x4+x5+x6<=65电饭煲：x7+x8+x9+x10<=62（2）每种产品计划内的销售量应该介于已签约的量，已签约量和意向签约量之间:xi-yi>=zi，xi-yi<=zi+pi（3）计划外的每种产品的销售量应该小于可能签订订购合同的最大合同量:yi<=ki（4）每种产品总的销售额小于已签约量，意向签约量，计划外销售量三者之和：xi<=zi+pi+ki然后应用LinGo软件编程（程序见附录二）可得结果公司的利润最大为1209.685元（二）问题（2）与问题1相似，为了使销售部的利润达到极大化，同样需要建立一个目标最大化模型，：营销部的收入＝经费+计划外销售额—计划外成本－上缴利润－宣传费约束条件（1）而各种产品的生产量不能超过其最大生产能力热水壶：x1+x2+x3<=50豆浆机：x4+x5+x6<=65电饭煲：x7+x8+x9+x10<=62（2）每种产品计划内的销售量应该介于已签约的量，已签约量和意向签约量之间:xi-yi>=zi，xi-yi<=zi+pi（3）计划外的每种产品的销售量应该小于可能签订订购合同的最大合同量:yi<=ki（3）每种产品总的销售额小于已签约量，意向签约量，计划外销售量三者之和：xi<=zi+pi+ki然后应用LinGo软件编程（程序见附录三）得出结果营销部的总收入极大为405.9621元。（三）问题（3）将公司和营销部看作一个整体来考虑,不用考虑营销部给公司上缴的那一部分利润，只考虑销售的总利润以及宣传费用，那么利润可以表示为：公司和营销部兼顾时的利润为＝总销售额－总成本－计划外产品的宣传费我们分别分析每种产品产量与成本关系表（表2），每种小家电的宣传费用随着销售量表(3)，每种小家电的销售额随订购量变化表（表4）用Matlab软件（运用三次拟合）编写程序可得：第i种产品的宣传费函数Qi(xi)；第i种产品的销售额函数Si(xi)；第i种产品的成本函数Fi(xi)，从而可得目标函数：M3=约束条件（1）因为各种产品的生产量不能超过其最大生产能力，所以有：热水壶：x1+x2+x3<=50豆浆机：x4+x5+x6<=65电饭煲：x7+x8+x9+x10<=62（2）每种产品计划内的销售量应该介于已签约的量，已签约量和意向签约量之间:xi-yi>=zi，xi-yi<=zi+pi（3）计划外的每种产品的销售量应该小于可能签订订购合同的最大合同量:yi<=ki（4）计划外的每种产品的总销售量总是不大于计划内每种产品的总销售额：yi<=xi然后应用LinGo软件编程（程序见附录四）得出结果：兼顾公司和营销部的利益时，最大利润为2155.776元。（四）问题（4）兼顾公司、营销部的利益以及客户的需求，尽量做到均衡销售时，我们要考虑到客户的需求，即要求客户的需求概率，这里用数学期望来解决，在问题（3）基础上，约束条件应该考虑客户期望，那么目标函数为：M4=约束条件（1）因为各种产品的生产量不能超过其最大生产能力，所以有：热水壶：x1+x2+x3<=50豆浆机：x4+x5+x6<=65电饭煲：x7+x8+x9+x10<=62（2）每种产品计划内的销售量应该介于已签约的量，已签约量和意向签约量之间:xi-yi>=zi，xi-yi<=zi+pi（3）通过对意向用户和计划外需求的概率表分析，根据期望计算公式E(X)=X1*p(X1)+X2*p(X2)+……+Xn*p(Xn)X1,X2,X3,……,Xn为这几个数据，p(X1),p(X2),p(X3),……p(Xn)为这几个数据的概率函数表各产品的需求期望单位（千件）产品12345678910期望3.6503.2503.0503.9504.7501.8004.3008.0003.7003.900所以xi<=zi+ui然后应用LinGo软件编程（程序见附录五）得出结果兼顾公司营销部的利益以及客户的需求，尽量做到均衡销售时，利润最大为1025.885元。（五）问题（5）营销部在计划外自行定价，在问题（4）的基础上，计划内的订购量已经确定，只是计划外的销售量随定价的变化变化，用Matlab软件（运用三次拟合）编写程序可得M5=约束条件（1）因为各种产品的生产量不能超过其最大生产能力，所以有：热水壶：x1+x2+x3<=50豆浆机：x4+x5+x6<=65电饭煲：x7+x8+x9+x10<=62（2）计划外的每种产品的总销售量总是不大于计划内每种产品的总销售额：yi<=xi（3）每种产品计划内的销售量应该等于已签约的量：xi-yi=zi然后应用LinGo软件编程（程序见附录六）得出结果模型解释为了便于比较，我们分别对五个问题列表进行解释如下，（单位：千）问题（1）表格1第i种产品的总销售量xi12241417.31627.80719.87615.01927.43713.6875.856计划外第i种产品的销售量yi4442.3162.8072.8760.0190.4370.6870.856问题（2）表格2第i种产品的总销售量xi1127121529201526138计划外第i种产品的销售量yi0400434533问题（3）表格3第i种产品的总销售量xi827151629201132145计划外第i种产品的销售量yi04445305310问题（4）表格4第i种产品的总销售量xi823.6513.0514.9524.7516.815.32513.75.163计划外第i种产品的销售量yi0000000000问题（5）表格5第i种产品的总销售量xi12.68727.312101022.1132.811.017295计划外第i种产品的销售量yi4.6877.312002.1117.800190模型应用与推广本问题是一个优化问题，通过对问题的分析建立了多个优化模型，可以推广到其他优化模型中，但是要根据实际情况进行假设，要注意条件的改变和现实情况的不同，建立真正适用的模型。参考文献（1）王连堂《数学建模》

陕西师范大学出版（2）文波《数学建模及其基础知识详解》（3）陈怀申《MATLAB及其在理工课程中的应用指南》西安电子科技大学出版社 附录一表110种小家电的“已签约合同量”以及“意向签约量”表序号12345678910家电名称1.5升热水壶1.8升热水壶2升热水壶0.9升豆浆机1.1升豆浆机1.3升豆浆机2升电饭煲2．5升电饭煲3升电饭煲3.5升电饭煲已签约量（万个）0.82.01.01.02.01.00.5意向签约量（万个）0.41.00.30.4表210种小家电产量与成本关系表产量（千件）家电1357101520253035401924.339.653.5572.9102.6129.6153175.5195.3208.829.826.4643.1258.3179.38111.7141.2166.6191.1208.3227.4310.227.5444.8860.6982.62116.3146.9173.4198.9221.3236.642366.55104.6140.1188.6265.7335.8391441.6491.1515.2526.575.52120.6161.4217.3298.1386.9450.5508.8565.8593.6627.277.52123.6165.6223.1314.2397.1462.4522.2580.7609.372879.8126166.6224315380.8434462509.656083085.5135178.5240337.5408465495546600931.790.3142.6188.6253.6356.6431.1491.3523.1576.96341032.592.146.2193.4260365.6442503.7536.2591.5650说明：表2中的数据为每种家电在相应产量下的总成本（单位：万元）。表3每种小家电的宣传费用随着销售量变化表产量（千件）家电13571015202530354010.882.333.634.766.288.6910.9812.9614.7416.4117.5420.962.543.965.196.839.4611.9614.1116.0517.4919.1312.644.125.397.119.8512.4414.6916.7118.5919.8742.256.389.5912.4516.2322.5128.4533.1237.0941.2543.2752.67.2411.0614.3418.7125.2532.7738.1642.7447.5249.8662.677.4311.3314.7219.2126.6133.6339.1643.8648.7851.1872.747.6511.5614.8119.2826.6732.2636.7638.8142.8147.0482.948.1912.3815.8720.6628.5934.5639.3841.5845.8650.493.118.6613.0816.7621.8330.2136.5141.6243.9448.4653.26103.188.8213.4117.1922.3830.9737.4542.6645.0449.6954.6说明：表3中的数据为每种小家电在相应销售量下的宣传费用（单位：万元）。表4每种小家电的销售额随订购量变化表订购量（千件）家电1234567891011112.622.933.343.151.960.16875.782.189.794.3213.7225.336.346.656.588.797.6102.6314.2826.537.748.458.868.277.183.892.5101.6108432.261.891.2114.7137157.8177.9194.8210.9231.9246.2537.171.9103.5131.6158181.9204.9224.7245.1267.3283.3638.0874.4106.2134.9161.9186.9210.3230.4249.9274.4292.7739.275.3109.3137.9165.1188.7211.6230.8251.8275.5294.684280.2117.1147.8176.8202.3226.7248.7270.3295.2314.9944.3884.8123.7156.1186.8213.6239.5252.9275.2311.9331.81045.586.9126159.6191.5219245.6269.4292.1319.8341.3说明：表4中的数据为每种小家电在相应订购量下的销售额（单位：万元）。表5八个签约订单的签约量表家电订单1234567891010.4820.50.3530.350.450.20.450.450.350.0740.250.350.250.350.10.1560.40.30.270.650.3580.950.5说明：表5中的数据为已签约的每个订单中对应小家电的数量（单位：万个）。表6五家意向签约客户的最大意向签约量表（万个）家电意向客户1234567891050.2表7意向客户1可能签订订购合同量的概率表家电签约量（万个）1234567891000.250.2表8意向客户2可能签订订购合同量的概率表家电签约量（万个）1234567891000.1表9意向客户3可能签订订购合同量的概率表家电签约量（万个）1234567891000.30.1表10意向客户4可能签订订购合同量的概率表家电签约量（万个）1234567891000.400.10.350.2表11意向客户5可能签订订购合同量的概率表家电签约量（万个）1234567891000.20.350.1表12计划外可能签订订购合同量的概率表产品合同量1234567891000.10.0表13企业向营销部发放计划内销售产品的经费（万元）表销售量（千件）家电13571015202530354011.8724.686.3967.5148.73611.1814.14416.69218.25220.33221.73622.03845.11686.95768.21089.474412.2215.39218.219.86421.63223.60832.12165.28327.23848.53329.869612.68816.06818.92820.69623.03624.59644.78412.81816.84819.65622.51629.01636.71242.69245.91651.06453.5655.51214.54919.44822.622632.55242.22449.19252.93658.81261.72465.657614.91319.91623.24426.67634.3243.36850.49254.28860.37263.33675.82415.3420.33223.426.7834.37241.647.37248.04852.98858.2486.2416.43221.73625.06428.70436.86844.56450.75251.4856.78462.496.593617.36822.98426.46830.31638.94847.0653.66454.39260.00865.936106.7617.6823.55627.14431.09639.93648.25655.01655.74461.51667.6表14计划外销售部分营销部向企业缴纳利润表销售量（千件）家电123456789101112.163.755.46.697.388.1158.679.429.6910.0810.47622.3524.3025.9047.0868.0288.6319.4749.76210.16410.93211.25332.4484.5786.0967.3148.3529.099.2469.4810.31411.38812.21845.5210.21514.7917.47519.4421.2722.6823.12424.28225.98026.50856.3612.53416.78820.12422.4424.5426.126.80227.8583031.10466.52813.22417.20820.60422.9825.3826.8227.38429.38230.78032.02876.7212.8417.72123.4625.442728.12229.36430.932.64087.213.4718.9622.5325.0827.3328.9229.8230.5133.1234.44097.60814.2820.0423.7926.5228.830.5431.58431.96233.7835.760107.814.7920.424.327.1829.5231.3232.2832.5834.6837.308附录二问题一的程序Max=(0.0003*(x1-y1)*(x1-y1)*(x1-y1)-0.2720*(x1-y1)*(x1-y1)+11.4429*(x1-y1)+1.3576+0.0078*(x2-y2)*(x2-y2)*(x2-y2)-0.4139*(x2-y2)*(x2-y2)+12.8769*(x2-y2)+1.2185+0.0165*(x3-y3)*(x3-y3)*(x3-y3)-0.5603*(x3-y3)*(x3-y3)+13.9414*(x3-y3)+0.7558+0.0682*(x4-y4)*(x4-y4)*(x4-y4)-1.9654*(x4-y4)*(x4-y4)+36.0104*(x4-y4)-2.0803+0.0584*(x5-y5)*(x5-y5)*(x5-y5)-1.9019*(x5-y5)*(x5-y5)+39.7564*(x5-y5)-0.5955+0.0783*(x6-y6)*(x6-y6)*(x6-y6)-2.2395*(x6-y6)*(x6-y6)+41.9655*(x6-y6)-1.5942+0.1045*(x7-y7)*(x7-y7)*(x7-y7)-2.7425*(x7-y7)*(x7-y7)+44.6484*(x7-y7)-3.1439+0.0985*(x8-y8)*(x8-y8)*(x8-y8)-2.7237*(x8-y8)*(x8-y8)+46.9763*(x8-y8)-2.6833+0.1870*(x9-y9)*(x9-y9)*(x9-y9)-4.3020*(x9-y9)*(x9-y9)+55.7898*(x9-y9)-9.0291+0.1048*(x10-y10)*(x10-y10)*(x10-y10)-2.9051*(x10-y10)*(x10-y10)+50.6082*(x10-y10)-2.7303)-(0.0002*(x1-y1)*(x1-y1)*(x1-y1)-0.0735*(x1-y1)*(x1-y1)+7.7904*(x1-y1)+1.8542+0.0005*(x2-y2)*(x2-y2)*(x2-y2)-0.0949*(x2-y2)*(x2-y2)+8.7093*(x2-y2)+1.4070+0.0002*(x3-y3)*(x3-y3)*(x3-y3)-0.0834*(x3-y3)*(x3-y3)+8.8314*(x3-y3)+2.0939+0.0004*(x4-y4)*(x4-y4)*(x4-y4)-0.2036*(x4-y4)*(x4-y4)+20.3812*(x4-y4)+5.7324-0.2010*(x5-y5)*(x5-y5)+22.8334*(x5-y5)+8.0202+0.0005*(x6-y6)*(x6-y6)*(x6-y6)-0.2436*(x6-y6)*(x6-y6)+24.1736*(x6-y6)+6.2363+0.0065*(x7-y7)*(x7-y7)*(x7-y7)-0.6369*(x7-y7)*(x7-y7)+29.0853*(x7-y7)-3.4501+0.007*(x8-y8)*(x8-y8)*(x8-y8)-0.6824*(x8-y8)*(x8-y8)+31.1628*(x8-y8)-3.6965+0.0073*(x9-y9)*(x9-y9)*(x9-y9)-0.7210*(x9-y9)*(x9-y9)+32.9269*(x9-y9)-3.9249+0.0076*(x10-y10)*(x10-y10)*(x10-y10)-0.7409*(x10-y10)*(x10-y10)+33.7974*(x10-y10)-4.2823)+(0.007*y1*y1*y1-0.2024*y1*y1+2.3288*y1-0.0140+0.0101*y2*y2*y2-0.2572*y2*y2+2.6463*y2-0.0346+0.0189*y3*y3*y3-0.3986*y3*y3+3.2644*y3-0.4915+0.0293*y4*y4*y4-0.7339*y4*y4+7.0365*y4-0.8632+0.0367*y5*y5*y5-0.8843*y5*y5+8.2061*y5-0.8670+0.0354*y6*y6*y6-0.8631*y6*y6+8.1944*y6-0.5351+0.0387*y7*y7*y7-0.9269*y7*y7+8.5683*y7-0.9010+0.0435*y8*y8*y8-1.0373*y8*y8+9.4151*y8-1.3150+0.0446*y9*y9*y9-1.0910*y9*y9+9.9706*y9-1.4294+0.0498*y10*y10*y10-1.1772*y10*y10+10.4393*y10-1.6511)-(0.0001*(x1-y1)*(x1-y1)*(x1-y1)-0.0136*(x1-y1)*(x1-y1)+0.8422*(x1-y1)+1.8398+0.0002*(x2-y2)*(x2-y2)*(x2-y2)-0.0163*(x2-y2)*(x2-y2)+0.9403*(x2-y2)+1.9451+0.0001*(x3-y3)*(x3-y3)*(x3-y3)-0.0153*(x3-y3)*(x3-y3)+0.9539*(x3-y3)+2.0766+0.0003*(x4-y4)*(x4-y4)*(x4-y4)-0.0363*(x4-y4)*(x4-y4)+2.1923*(x4-y4)+4.9782+0.0003*(x5-y5)*(x5-y5)*(x5-y5)-0.0385*(x5-y5)*(x5-y5)+2.4607*(x5-y5)+5.8576+0.0004*(x6-y6)*(x6-y6)*(x6-y6)-0.0437*(x6-y6)*(x6-y6)+2.6104*(x6-y6)+5.7752+0.0010*(x7-y7)*(x7-y7)*(x7-y7)-0.0844*(x7-y7)*(x7-y7)+3.1029*(x7-y7)+4.9506+0.0011*(x8-y8)*(x8-y8)*(x8-y8)-0.0906*(x8-y8)*(x8-y8)+3.3277*(x8-y8)+5.2847+0.0011*(x9-y9)*(x9-y9)*(x9-y9)-0.0954*(x9-y9)*(x9-y9)+3.5112*(x9-y9)+5.5989+0.0012*(x10-y10)*(x10-y10)*(x10-y10)-0.0984*(x10-y10)*(x10-y10)+3.6110*(x10-y10)+5.6761);x1+x2+x3<=50;x4+x5+x6<=65;x7+x8+x9+x10<=62;x1-y1<=11;x2-y2<=23;x3-y3<=12;x4-y4<=15;x5-y5<=25;x6-y6<=17;x7-y7<=15;x8-y8<=27;x9-y9<=13;x10-y10<=9;y1<=4;y2<=4;y3<=4;y4<=4;y5<=4;y6<=3;y7<=4;y8<=5;y9<=3;y10<=3;x1<=15;x2<=27;x3<=16;x4<=19;x5<=29;x6<=20;x7<=20;x8<=32;x9<=16;x10<=12;x1-y1>=8;x2-y2>=20;x3-y3>=10;x4-y4>=10;x5-y5>=20;x6-y6>=15;x7-y7>=11;x8-y8>=17;x9-y9>=10;x10-y10>=5;y1<=x1;y2<=x2;y3<=x3;y4<=x4;y5<=x5;y6<=x6;y7<=x7;y8<=x8;y9<=x9;y10<=x10;end运行结果Localoptimalsolutionfound.Objectivevalue:1209.685Extendedsolversteps:3Totalsolveriterations:9507VariableValueReducedCostX112.000000.000000Y14.0000000.000000X224.000000.000000Y24.0000000.000000X314.000000.000000Y34.0000000.000000X417.316260.000000Y42.3162610.000000X527.807750.000000Y52.8077510.000000X619.875990.000000Y62.8759890.000000X715.018980.000000Y70.1897651E-010.000000X827.437130.000000Y80.43713160.000000X913.687780.000000Y90.68777690.000000X105.8561150.000000Y100.85611490.000000RowSlackorSurplusDualPrice11209.6851.00000020.0000000.00000030.0000004.10828240.0000008.53316353.0000000.00000063.0000000.00000072.0000000.00000080.0000003.12611890.00000036.17152100.00000011.80422110.0000008.766037120.00000096.31964130.00000010.74314144.0000000.000000150.0000001.045600160.0000001.073500170.0000000.9828000181.6837390.000000191.1922490.000000200.12401140.000000213.9810230.000000224.5628680.000000232.3122230.000000242.1438850.000000253.0000000.000000263.0000000.000000272.0000000.000000281.6837390.000000291.1922490.000000300.12401140.000000314.9810230.000000324.5628680.000000332.3122230.000000346.1438850.000000350.000000-0.1481000360.000000-0.3607000370.000000-0.2159000385.0000000.000000395.0000000.000000402.0000000.000000414.0000000.0000004210.000000.000000433.0000000.000000440.000000-8.791363458.0000000.0000004620.000000.0000004710.000000.0000004815.000000.0000004925.000000.0000005017.000000.0000005115.000000.0000005227.000000.0000005313.000000.000000545.0000000.000000附录三问题（2）Max=(0.0001*(x1-y1)*(x1-y1)*(x1-y1)-0.0136*(x1-y1)*(x1-y1)+0.8422*(x1-y1)+1.8398+0.0002*(x2-y2)*(x2-y2)*(x2-y2)-0.0163*(x2-y2)*(x2-y2)+0.9403*(x2-y2)+1.9451+0.0001*(x3-y3)*(x3-y3)*(x3-y3)-0.0153*(x3-y3)*(x3-y3)+0.9539*(x3-y3)+2.0766+0.0003*(x4-y4)*(x4-y4)*(x4-y4)-0.0363*(x4-y4)*(x4-y4)+2.1923*(x4-y4)+4.9782+0.0003*(x5-y5)*(x5-y5)*(x5-y5)-0.0385*(x5-y5)*(x5-y5)+2.4607*(x5-y5)+5.8576+0.0004*(x6-y6)*(x6-y6)*(x6-y6)-0.0437*(x6-y6)*(x6-y6)+2.6104*(x6-y6)+5.7752+0.0010*(x7-y7)*(x7-y7)*(x7-y7)-0.0844*(x7-y7)*(x7-y7)+3.1029*(x7-y7)+4.9506+0.0011*(x8-y8)*(x8-y8)*(x8-y8)-0.0906*(x8-y8)*(x8-y8)+3.3277*(x8-y8)+5.2847+0.0011*(x9-y9)*(x9-y9)*(x9-y9)-0.0954*(x9-y9)*(x9-y9)+3.5112*(x9-y9)+5.5989+0.0012*(x10-y10)*(x10-y10)*(x10-y10)-0.0984*(x10-y10)*(x10-y10)+3.6110*(x10-y10)+5.6761)+0.0003*y1*y1*y1-0.2720*y1*y1+11.4429*y1+1.3576+0.0078*y2*y2*y2-1.9654*y2*y2+36.0104*y2-2.0803+0.0165*y3*y3*y3-0.0078*y3*y3+0.7456*y3+0.4289+0.0682*y4*y4*y4-0.0192*y4*y4+1.7226*y4+1.0658-0.0584*y5*y5*y5-1.9019*y5*y5+39.7564*y5-0.5955+0.0783*y6*y6*y6-2.2395*y6*y6+41.9655*y6-1.5942+0.1045*y7*y7*y7-2.7425*y7*y7+44.6484*y7-3.1439+0.0985*y8*y8*y8-2.7237*y8*y8+46.9763*y8-2.6833+0.1870*y9*y9*y9-4.3020*y9*y9+55.7898*y9-9.0291+0.1048*y10*y10*y10-2.9051*y10*y10+50.6082*y10-2.7303-(0.0070*y1*y1*y1-0.2024*y1*y1+2.3288*y1-0.0140+0.0101*y2*y2*y2-0.2572*y2*y2+2.6463*y2-0.0346+0.0189*y3*y3*y3-0.3986*y3*y3+3.2644*y3-0.4915+0.0293*y4*y4*y4-0.7339*y4*y4+7.0365*y4-0.8632+0.0367*y5*y5*y5-0.8843*y5*y5+8.2061*y5-0.8670+0.0353*y6*y6*y6-0.8619*y6*y6+8.1866*y6-0.5205+0.0387*y7*y7*y7-0.9269*y7*y7+8.5683*y7-0.9010+0.0435*y8*y8*y8-1.0373*y8*y8+9.4151*y8-1.3150+0.0446*y9*y9*y9-1.0910*y9*y9+9.9706*y9-1.4294+0.0498*y10*y10*y10-1.1772*y10*y10+10.4393*y10-1.6511)-(0.0000*x1*x1*x1-0.0070*x1*x1+0.6594*x1+0.3739+0.0001*x2*x2*x2-0.0089*x2*x2+0.7367*x2+0.3601+0.0000-0.0078*x3*x3+0.7456*x3+0.4289+0.0001*x4*x4*x4-0.0192*x4*x4+1.7226*x4+1.0658-0.0001*x5*x5*x5-0.0150*x5*x5+1.8778*x5+1.4710+0.0001*x6*x6*x6-0.0229*x6*x6+2.0429*x6+1.2159+0.0006*x7*x7*x7-0.0559*x7*x7+2.4528*x7+0.4251+0.0006*x8*x8*x8-0.0600*x8*x8+2.6299*x8+0.4499+0.0007*x9*x9*x9-0.0633*x9*x9+2.7770*x9+0.4818+0.0007*x10*x10*x10-0.0651*x10*x10+2.8525*x10+0.4609)-(0.0002*x1*x1*x1-0.0735*x1*x1+7.7904*x1+1.8542+0.0005*x2*x2*x2-0.0949*x2*x2+8.7093*x2+1.4070+0.0002*x3*x3*x3-0.0834*x3*x3+8.8314*x3+2.0939+0.0004*x4*x4*x4-0.2036*x4*x4+20.3812*x4+5.7324-0.2010*x5*x5+22.8334*x5+8.0202+0.0005*x6*x6*x6-0.2436*x6*x6+24.1736*x6+6.2363+0.0065*x7*x7*x7-0.6369*x7*x7+29.0853*x7-3.4501+0.007*x8*x8*x8-0.6824*x8*x8+31.1628*x8-3.6965+0.0073*x9*x9*x9-0.7210*x9*x9+32.9269*x9-3.9249+0.0076*x10*x10*x10-0.7409*x10*x10+33.7974*x10-4.2823)*(y1+y2+y3+y4+y5+y6+y7+y8+y9+y10)/(x1+x2+x3+x4+x5+x6+x7+x8+x9+x10);x1+x2+x3<=50;x4+x5+x6<=65;x7+x8+x9+x10<=62;x1-y1<=11;x2-y2<=23;x3-y3<=12;x4-y4<=15;x5-y5<=25;x6-y6<=17;x7-y7<=15;x8-y8<=27;x9-y9<=13;x10-y10<=9;y1<=4;y2<=4;y3<=4;y4<=4;y5<=4;y6<=3;y7<=4;y8<=5;y9<=3;y10<=3;x1<=15;x2<=27;x3<=16;x4<=19;x5<=29;x6<=20;x7<=20;x8<=32;x9<=16;x10<=12;x1-y1>=8;x2-y2>=20;x3-y3>=10;x4-y4>=10;x5-y5>=20;x6-y6>=15;x7-y7>=11;x8-y8>=17;x9-y9>=10;x10-y10>=5;y1<=x1;y2<=x2;y3<=x3;y4<=x4;y5<=x5;y6<=x6;y7<=x7;y8<=x8;y9<=x9;y10<=x10;end运行结果Localoptimalsolutionfound.Objectivevalue:405.9621Extendedsolversteps:2Totalsolveriterations:3023VariableValueReducedCostX111.000000.000000Y10.0000006.054804X227.000000.000000Y24.0000000.000000X312.000000.000000Y30.00000017.83971X415.000000.000000Y40.00000022.41723X529.000000.000000Y54.0000000.000000X620.000000.000000Y63.0000000.000000X715.000000.000000Y74.0000000.000000X826.000000.000000Y85.0000000.000000X913.000000.000000Y93.0000000.000000X108.0000000.000000Y103.0000000.000000RowSlackorSurplusDualPrice1405.96211.00000020.0000000.00000031.0000000.00000040.0000001.17417950.0000001.53293460.0000001.72374170.0000001.43152780.0000000.325011390.0000001.073527100.0000000.3859568114.0000000.000000126.0000000.000000133.0000000.000000144.0000000.000000154.0000000.000000160.0000004.681403174.0000000.000000184.0000000.000000190.0000002.697489200.0000009.466319210.0000006.495701220.0000007.721862230.00000011.35526240.00000010.96908254.0000000.000000260.0000000.000000274.0000000.000000284.0000000.000000290.0000000.000000300.0000000.000000315.0000000.000000326.0000000.000000333.0000000.000000344.0000000.000000353.0000000.000000363.0000000.000000372.0000000.000000385.0000000.000000395.0000000.000000402.0000000.000000410.000000-0.4863614424.0000000.000000430.000000-0.9870000440.000000-1.4778844511.000000.0000004623.000000.0000004712.000000.0000004815.000000.0000004925.000000.0000005017.000000.0000005111.000000.0000005221.000000.0000005310.000000.000000545.0000000.000000附录四程序Max=0.0003*x1*x1*x1-0.2720*x1*x1+11.4429*x1+1.3576+0.0078*x2*x2*x2-0.4139*x2*x2+12.8769*x2+1.2185+0.0165*x3*x3*x3-0.5603*x3*x3+13.9414*x3+0.7558+0.0682*x4*x4*x4-1.9654*x4*x4+36.0104*x4-2.0803+0.0584*x5*x5*x5-1.9019*x5*x5+39.7564*x5-0.5955+0.0783*x6*x6*x6-2.2395*x6*x6+41.9655*x6-1.5942+0.1045*x7*x7*x7-2.7425*x7*x7+44.6484*x7-3.1439+0.098