企業(yè)的營銷管理問題-畢業(yè)論文

PAGEPAGE29企業(yè)的營銷管理問題（物理系：段文瑞數(shù)學(xué)系：張曄韓瑩）摘要本文屬于企業(yè)的營銷管理優(yōu)化問題，主要解決的是公司最大利潤、營銷部的最大收入等問題。通過對影響公司利潤，營銷部收入的因素如公司的生產(chǎn)成本、宣傳費用、意向訂單、客戶資料等的分析以及對問題的整體把握，由于最大生產(chǎn)能力的制約，我們需要在滿足已簽約的銷售合同的基礎(chǔ)上，對意向簽約量有選擇的安排生產(chǎn)，使公司的利潤達(dá)到最大，而營銷部應(yīng)盡力爭取與意向客戶的簽訂合同，爭取多銷售產(chǎn)品時，可使總收入極大化。我們先假設(shè)在理想情況下即客戶意向為100%情況下求解出方案，然后一一考慮不同客戶的意向需求量，根據(jù)不同商家的期望值，及產(chǎn)品的不同利潤有選擇的進(jìn)行生產(chǎn)。本問題中我們使用非線性規(guī)劃求最優(yōu)解的方法并利用MATLAB和LinGo軟件進(jìn)行求解。得出問題（1）中公司的利潤最大為1209.685元；問題（2）營銷部總收入極大為405.9621元；問題（3）兼顧公司和營銷部二者的利益為元；問題（4）兼顧公司、營銷部的利益以及客戶的需求，盡量做到均衡銷售時的利潤最大為元；問題（4）使?fàn)I銷部總收入最大的定價、生產(chǎn)及銷售關(guān)鍵字利潤非線性規(guī)劃最優(yōu)解擬合問題重述任何一個企業(yè)都面臨著將產(chǎn)品推向市場，銷售出去。一般的，企業(yè)下設(shè)營銷部，通過營銷部對企業(yè)生產(chǎn)的產(chǎn)品進(jìn)行銷售。由于企業(yè)生產(chǎn)能力的制約，需要在滿足已簽約的銷售合同量的基礎(chǔ)上，對意向簽約量有選擇的安排生產(chǎn)。一方面，企業(yè)會組織安排生產(chǎn)，完成已簽約的銷售合同；另一方面，企業(yè)希望營銷部門盡力爭取與意向簽約的客戶簽訂正式銷售合同；除此之外，企業(yè)還希望營銷部門努力再多銷售一些產(chǎn)品（計劃外）。對于所簽約的銷售合同和意向簽約量（計劃內(nèi)），企業(yè)根據(jù)銷售量向營銷部發(fā)放經(jīng)費（包括工資以及宣傳費用等）；對于計劃外銷售的產(chǎn)品，實行承包制，營銷部向企業(yè)繳納利潤。產(chǎn)品的生產(chǎn)費用由企業(yè)承擔(dān)，與銷售有關(guān)的費用（如產(chǎn)品的宣傳費用等）由營銷部承擔(dān)。宏宇電器公司2011年計劃生產(chǎn)三類10種小家電，其中包括：熱水壺（1.5升，1.8升，2升）、豆?jié){機（0.9升，1.1升，1.3升）、電飯煲（2升三類小家電的年最大生產(chǎn)能力分別為：熱水壺：5萬個；豆?jié){機：6.5萬個；電飯煲6.2萬個。相關(guān)的各類數(shù)據(jù)見附錄一（表1至表14）分別按以下要求為宏宇電器公司制定相應(yīng)的生產(chǎn)、銷售方案：（1）使公司的利潤達(dá)到最大；（2）使?fàn)I銷部的總收入極大化；（3）兼顧公司和營銷部二者的利益；（4）兼顧公司、營銷部的利益以及客戶的需求，盡量做到均衡銷售；（5）公司為了調(diào)動營銷部的積極性，為公司多創(chuàng)利潤，規(guī)定對于計劃外銷售的產(chǎn)品，營銷部可以自行定價。統(tǒng)計數(shù)據(jù)顯示，自行定價后每單位產(chǎn)品的銷售價格上漲或下降5％，則三類小家電的可能銷售量相應(yīng)的減少或增加10％。試確定使?fàn)I銷部總收入最大的定價、生產(chǎn)及銷售方案。問題分析問題（1）（2）中要求根據(jù)給出的相關(guān)數(shù)據(jù)建立模型求出最佳的生產(chǎn)、銷售方案，分別使公司的利潤達(dá)到最大和營銷部的總收入極大化。通過對表分析，我們知道產(chǎn)品在計劃內(nèi)銷售時帶給公司的利潤要大于將其在計劃外銷售所帶來的利潤益，那么必然要使計劃內(nèi)的訂單訂購量足夠大（但不能超出最大生產(chǎn)能力），我們假設(shè)按訂單的最大意向簽約量簽約有簽約意向的客戶，此時計劃內(nèi)的訂夠量最大。對于問題（3）在兼顧公司和營銷部二者的利益時，把兩者看作一個整體建立模型求出最佳的生產(chǎn)、銷售方案，那么此時就不用考慮營銷部給公司上繳的那一部分利潤，只考慮銷售的總利潤以及宣傳費用問題（4）當(dāng)兼顧公司、營銷部的利益以及客戶的需求時，需要考慮顧客的要求，即要求客戶的需求概率，這里用數(shù)學(xué)期望來解決問題（5）產(chǎn)品的銷量與產(chǎn)品單價有一定的關(guān)系，故提高或降低價格會減少或增加銷量，利用MATLAB求出目標(biāo)函數(shù)的最優(yōu)解，即營銷部的最大總收入，同時求出每種產(chǎn)品價格上漲率的具體值，從而確定營銷部的定價方案。模型假設(shè)（1）假設(shè)客戶的訂購量就是生產(chǎn)量，生產(chǎn)量就是銷售量；（2）與銷售有關(guān)的經(jīng)費只考慮宣傳費用，其他費用不考慮；（3）營銷部除了只給企業(yè)上繳利潤和承擔(dān)宣傳費用外，無其他費用支出；（4）假設(shè)問題（1）（2）（3）中，將意向客戶的需求概率設(shè)為100%；（5）該企業(yè)周圍的各種因素都是穩(wěn)定的符號說明xi第i種產(chǎn)品的總銷售量i=1，2···10yi計劃外第i種產(chǎn)品的銷售量i=1，2···10zi第i中產(chǎn)品的已簽約量i=1，2···10pi第i中產(chǎn)品的意向簽約量i=1，2···10ki第i種產(chǎn)品可能簽訂訂購合同的最大合同量；i=1，2···10Qi(xi)第i種產(chǎn)品的宣傳費函數(shù)i=1，2···10Si(xi)第i種產(chǎn)品的銷售額函數(shù)i=1，2···10Ui第i種產(chǎn)品的的需求期望i=1，2···10Mi（yi）計劃外第i中產(chǎn)品的銷售額i=1，2···10Ti(yi)計劃外第i種產(chǎn)品的上繳利潤函數(shù)i=1，2···10Fi(xi)第i種產(chǎn)品的成本函數(shù)i=1，2···10Si(xi-yi)計劃內(nèi)第i種產(chǎn)品的銷售額函數(shù)i=1，2···10Fi(xi-yi)計劃內(nèi)第i種產(chǎn)品的成本函數(shù)i=1，2···10Ni(xi-yi)計劃內(nèi)第i種產(chǎn)品的銷售部經(jīng)費函數(shù)i=1，2···10Hi（yi(1-0.1S)）計劃外的第i種產(chǎn)品價格改變后的銷售額函數(shù)i=1，2···10Bi（yi(1-0.1S)）價格改變后的第i種產(chǎn)品的上繳利潤函數(shù)i=1，2···10模型的建立與求解（一）問題（1）我們可以知道公司利潤就是計劃內(nèi)的利潤和計劃外的利潤之和，那公司的贏利可以表示為：公司利潤＝計劃內(nèi)銷售額+計劃外上繳利潤－計劃內(nèi)成本－計劃外營銷部經(jīng)費我們分別分析每種產(chǎn)品產(chǎn)量與成本關(guān)系表（表2），每種小家電的銷售額隨訂購量變化(表4），計劃外銷售部分營銷部向企業(yè)繳納利潤表(表14);用Matlab軟件（運用三次擬合）編寫程序，可以得出第i種產(chǎn)品的銷售額函數(shù)Si(xi-yi)；計劃外第i種產(chǎn)品的上繳利潤函數(shù)Ti(yi)；計劃內(nèi)第i種產(chǎn)品的成本函數(shù)Fi(xi-yi)；計劃外銷售部經(jīng)費函數(shù)Ni(yi)根據(jù)述各種準(zhǔn)備可建立目標(biāo)函數(shù)M1=約束條件（1）因為各種產(chǎn)品的生產(chǎn)量不能超過其最大生產(chǎn)能力，所以可得:熱水壺：x1+x2+x3<=50豆?jié){機：x4+x5+x6<=65電飯煲：x7+x8+x9+x10<=62（2）每種產(chǎn)品計劃內(nèi)的銷售量應(yīng)該介于已簽約的量，已簽約量和意向簽約量之間:xi-yi>=zi，xi-yi<=zi+pi（3）計劃外的每種產(chǎn)品的銷售量應(yīng)該小于可能簽訂訂購合同的最大合同量:yi<=ki（4）每種產(chǎn)品總的銷售額小于已簽約量，意向簽約量，計劃外銷售量三者之和：xi<=zi+pi+ki然后應(yīng)用LinGo軟件編程（程序見附錄二）可得結(jié)果公司的利潤最大為1209.685元（二）問題（2）與問題1相似，為了使銷售部的利潤達(dá)到極大化，同樣需要建立一個目標(biāo)最大化模型，：營銷部的收入＝經(jīng)費+計劃外銷售額—計劃外成本－上繳利潤－宣傳費約束條件（1）而各種產(chǎn)品的生產(chǎn)量不能超過其最大生產(chǎn)能力熱水壺：x1+x2+x3<=50豆?jié){機：x4+x5+x6<=65電飯煲：x7+x8+x9+x10<=62（2）每種產(chǎn)品計劃內(nèi)的銷售量應(yīng)該介于已簽約的量，已簽約量和意向簽約量之間:xi-yi>=zi，xi-yi<=zi+pi（3）計劃外的每種產(chǎn)品的銷售量應(yīng)該小于可能簽訂訂購合同的最大合同量:yi<=ki（3）每種產(chǎn)品總的銷售額小于已簽約量，意向簽約量，計劃外銷售量三者之和：xi<=zi+pi+ki然后應(yīng)用LinGo軟件編程（程序見附錄三）得出結(jié)果營銷部的總收入極大為405.9621元。（三）問題（3）將公司和營銷部看作一個整體來考慮,不用考慮營銷部給公司上繳的那一部分利潤，只考慮銷售的總利潤以及宣傳費用，那么利潤可以表示為：公司和營銷部兼顧時的利潤為＝總銷售額－總成本－計劃外產(chǎn)品的宣傳費我們分別分析每種產(chǎn)品產(chǎn)量與成本關(guān)系表（表2），每種小家電的宣傳費用隨著銷售量表(3)，每種小家電的銷售額隨訂購量變化表（表4）用Matlab軟件（運用三次擬合）編寫程序可得：第i種產(chǎn)品的宣傳費函數(shù)Qi(xi)；第i種產(chǎn)品的銷售額函數(shù)Si(xi)；第i種產(chǎn)品的成本函數(shù)Fi(xi)，從而可得目標(biāo)函數(shù)：M3=約束條件（1）因為各種產(chǎn)品的生產(chǎn)量不能超過其最大生產(chǎn)能力，所以有：熱水壺：x1+x2+x3<=50豆?jié){機：x4+x5+x6<=65電飯煲：x7+x8+x9+x10<=62（2）每種產(chǎn)品計劃內(nèi)的銷售量應(yīng)該介于已簽約的量，已簽約量和意向簽約量之間:xi-yi>=zi，xi-yi<=zi+pi（3）計劃外的每種產(chǎn)品的銷售量應(yīng)該小于可能簽訂訂購合同的最大合同量:yi<=ki（4）計劃外的每種產(chǎn)品的總銷售量總是不大于計劃內(nèi)每種產(chǎn)品的總銷售額：yi<=xi然后應(yīng)用LinGo軟件編程（程序見附錄四）得出結(jié)果：兼顧公司和營銷部的利益時，最大利潤為2155.776元。（四）問題（4）兼顧公司、營銷部的利益以及客戶的需求，盡量做到均衡銷售時，我們要考慮到客戶的需求，即要求客戶的需求概率，這里用數(shù)學(xué)期望來解決，在問題（3）基礎(chǔ)上，約束條件應(yīng)該考慮客戶期望，那么目標(biāo)函數(shù)為：M4=約束條件（1）因為各種產(chǎn)品的生產(chǎn)量不能超過其最大生產(chǎn)能力，所以有：熱水壺：x1+x2+x3<=50豆?jié){機：x4+x5+x6<=65電飯煲：x7+x8+x9+x10<=62（2）每種產(chǎn)品計劃內(nèi)的銷售量應(yīng)該介于已簽約的量，已簽約量和意向簽約量之間:xi-yi>=zi，xi-yi<=zi+pi（3）通過對意向用戶和計劃外需求的概率表分析，根據(jù)期望計算公式E(X)=X1*p(X1)+X2*p(X2)+……+Xn*p(Xn)X1,X2,X3,……,Xn為這幾個數(shù)據(jù)，p(X1),p(X2),p(X3),……p(Xn)為這幾個數(shù)據(jù)的概率函數(shù)表各產(chǎn)品的需求期望單位（千件）產(chǎn)品12345678910期望3.6503.2503.0503.9504.7501.8004.3008.0003.7003.900所以xi<=zi+ui然后應(yīng)用LinGo軟件編程（程序見附錄五）得出結(jié)果兼顧公司營銷部的利益以及客戶的需求，盡量做到均衡銷售時，利潤最大為1025.885元。（五）問題（5）營銷部在計劃外自行定價，在問題（4）的基礎(chǔ)上，計劃內(nèi)的訂購量已經(jīng)確定，只是計劃外的銷售量隨定價的變化變化，用Matlab軟件（運用三次擬合）編寫程序可得M5=約束條件（1）因為各種產(chǎn)品的生產(chǎn)量不能超過其最大生產(chǎn)能力，所以有：熱水壺：x1+x2+x3<=50豆?jié){機：x4+x5+x6<=65電飯煲：x7+x8+x9+x10<=62（2）計劃外的每種產(chǎn)品的總銷售量總是不大于計劃內(nèi)每種產(chǎn)品的總銷售額：yi<=xi（3）每種產(chǎn)品計劃內(nèi)的銷售量應(yīng)該等于已簽約的量：xi-yi=zi然后應(yīng)用LinGo軟件編程（程序見附錄六）得出結(jié)果模型解釋為了便于比較，我們分別對五個問題列表進(jìn)行解釋如下，（單位：千）問題（1）表格1第i種產(chǎn)品的總銷售量xi12241417.31627.80719.87615.01927.43713.6875.856計劃外第i種產(chǎn)品的銷售量yi4442.3162.8072.8760.0190.4370.6870.856問題（2）表格2第i種產(chǎn)品的總銷售量xi1127121529201526138計劃外第i種產(chǎn)品的銷售量yi0400434533問題（3）表格3第i種產(chǎn)品的總銷售量xi827151629201132145計劃外第i種產(chǎn)品的銷售量yi04445305310問題（4）表格4第i種產(chǎn)品的總銷售量xi823.6513.0514.9524.7516.815.32513.75.163計劃外第i種產(chǎn)品的銷售量yi0000000000問題（5）表格5第i種產(chǎn)品的總銷售量xi12.68727.312101022.1132.811.017295計劃外第i種產(chǎn)品的銷售量yi4.6877.312002.1117.800190模型應(yīng)用與推廣本問題是一個優(yōu)化問題，通過對問題的分析建立了多個優(yōu)化模型，可以推廣到其他優(yōu)化模型中，但是要根據(jù)實際情況進(jìn)行假設(shè)，要注意條件的改變和現(xiàn)實情況的不同，建立真正適用的模型。參考文獻(xiàn)（1）王連堂《數(shù)學(xué)建?！?/p>

陜西師范大學(xué)出版（2）文波《數(shù)學(xué)建模及其基礎(chǔ)知識詳解》（3）陳懷申《MATLAB及其在理工課程中的應(yīng)用指南》西安電子科技大學(xué)出版社 附錄一表110種小家電的“已簽約合同量”以及“意向簽約量”表序號12345678910家電名稱1.5升熱水壺1.8升熱水壺2升熱水壺0.9升豆?jié){機1.1升豆?jié){機1.3升豆?jié){機2升電飯煲2．5升電飯煲3升電飯煲3.5升電飯煲已簽約量（萬個）0.82.01.01.02.01.00.5意向簽約量（萬個）0.41.00.30.4表210種小家電產(chǎn)量與成本關(guān)系表產(chǎn)量（千件）家電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說明：表2中的數(shù)據(jù)為每種家電在相應(yīng)產(chǎn)量下的總成本（單位：萬元）。表3每種小家電的宣傳費用隨著銷售量變化表產(chǎn)量（千件）家電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說明：表3中的數(shù)據(jù)為每種小家電在相應(yīng)銷售量下的宣傳費用（單位：萬元）。表4每種小家電的銷售額隨訂購量變化表訂購量（千件）家電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說明：表4中的數(shù)據(jù)為每種小家電在相應(yīng)訂購量下的銷售額（單位：萬元）。表5八個簽約訂單的簽約量表家電訂單1234567891010.4820.50.3530.350.450.20.450.450.350.0740.250.350.250.350.10.1560.40.30.270.650.3580.950.5說明：表5中的數(shù)據(jù)為已簽約的每個訂單中對應(yīng)小家電的數(shù)量（單位：萬個）。表6五家意向簽約客戶的最大意向簽約量表（萬個）家電意向客戶1234567891050.2表7意向客戶1可能簽訂訂購合同量的概率表家電簽約量（萬個）1234567891000.250.2表8意向客戶2可能簽訂訂購合同量的概率表家電簽約量（萬個）1234567891000.1表9意向客戶3可能簽訂訂購合同量的概率表家電簽約量（萬個）1234567891000.30.1表10意向客戶4可能簽訂訂購合同量的概率表家電簽約量（萬個）1234567891000.400.10.350.2表11意向客戶5可能簽訂訂購合同量的概率表家電簽約量（萬個）1234567891000.20.350.1表12計劃外可能簽訂訂購合同量的概率表產(chǎn)品合同量1234567891000.10.0表13企業(yè)向營銷部發(fā)放計劃內(nèi)銷售產(chǎn)品的經(jīng)費（萬元）表銷售量（千件）家電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計劃外銷售部分營銷部向企業(yè)繳納利潤表銷售量（千件）家電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附錄二問題一的程序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運行結(jié)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附錄三問題（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運行結(jié)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附錄四程序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