管理運(yùn)籌學(xué)之線性規(guī)劃與單純型法

7/29/20231管理運(yùn)籌學(xué)7/29/20232線性規(guī)劃與單純型法第二講7/29/20233由實(shí)際問(wèn)題引出數(shù)學(xué)模形。產(chǎn)品A產(chǎn)品B資源限量勞動(dòng)力設(shè)備原材料9434510360200300利潤(rùn)元/KG701201.確定決策變量:設(shè)生產(chǎn)A,B分別為x1,x22.確定目標(biāo)函數(shù):3.確定約束條件:一、LP問(wèn)題的基本概念7格/狂2耍0蚊/為2績(jī)0哪2淋34典傳型殘的L伶P問(wèn)夸題:一考、L習(xí)P問(wèn)磁題題的改基嫂本認(rèn)概漁念7姐/納2肢0樸/說(shuō)2體0謙2伸35用等向約量份符悟號(hào)嶼表逗示融為:用道向掩量齒和通矩愚陣判表?yè)p示總為:一蚊、L幸P問(wèn)糠題糞的摧基耕本禿概筐念7糊/仔2朋0域/棒2搶0允2紋361國(guó).基興、免基戒向改量董、違基透變攝量釘、壟非丙基偷變悟量設(shè)A為頁(yè)約哥束棋方輛程言組估的m縫×亡n階音系閃數(shù)施矩義陣湊，界其炎秩仿為m，B是A中悲的俊一兇個(gè)m階迫滿囑秩爛子而矩她陣位，擱稱B為L(zhǎng)帖P問(wèn)物題堅(jiān)的石一灑個(gè)基。B中烘每鴉一鞋個(gè)辱列能向塑量糟稱僅為基欠向王量，蘇對(duì)圖于蘋的里變仇量xj為基銜變徐量，插其荷余肌的懇變廚量要稱嚴(yán)為非貸基趙變婦量。一管、L棉P問(wèn)肆題啦的危基圍本部概暑念7政/贊2顏0拒/轉(zhuǎn)2崗0盒2挖371借.基腎、叮基快向暗量乏、逃基棟變揮量喊、扇非物基任變津量一米、L疏P問(wèn)只題歡的詳基菠本盾概框念7虧/咳2協(xié)0州/借2貧0莖2傻38滿穩(wěn)足信約招束生方個(gè)程(包懸括冒非棒負(fù)斷約尤束)的柿所前有束解卡，萄稱渡為可株行辦解鬼。對(duì)岸于利某助組運(yùn)選剩定蒜的益基決，令非乎基遞變部量揭為0，洽與碑約旨束老方遷程貞求舉得易的鮮唯蛾一兆解易，此稱位為基討解。2鹿.可芒行淹解筑、寄基艇解徒、敗基讀可窮行恨解蜂、熄可認(rèn)行晃基一焰、L鈴P問(wèn)之題朵的翼基傲本況概恐念7踐/觀2繡0塊/延2疤0淋2揚(yáng)39基憲解中死滿腿足卡所停有糠變擺量非品負(fù)約易束嗓的鍋解衡，芽稱著為基劫可眼行現(xiàn)解。2器.可焰行桶解糞、棒基桂解陳、責(zé)基漂可慎行雀解牢、逃可薪行無(wú)基與基俘可冶行好解對(duì)耽應(yīng)惕的拆基序稱紡為可推行綢基。一賓、L副P問(wèn)犯題吊的業(yè)基哨本纖概糟念7煌/證2京0藝/煎2積0部2話31更0概圣念緩練株習(xí):找秀出紀(jì)下預(yù)列L襪P問(wèn)阻題梁的尖全乳部珍基抵解懷。1234512345一之、L紀(jì)P問(wèn)典題罩的搖基場(chǎng)本睛概提念7驚/轟2近0耳/致2會(huì)0春2行31街1組合x1x2x3x4x5z基可行解？1-2001-3001-4001-5002-3002-4002-5003-4003-5004-50051045////55-120452175541010-5415////52.51.517.554-32224319×××××一股、L剛P問(wèn)瞧題亞的短基脖本拜概澤念7巨/許2梢0我/問(wèn)2縣0潛2貿(mào)31夠21什.連弱線:二膨、扇重霉要值定洲理細(xì)與槐引快理在n維E另u蠅c謙l僚i驗(yàn)d空葉間摟中凡，秤點(diǎn)X與Y連火線蝦上呆的辰點(diǎn)讀，忘是梳指咐如鬧下茅形說(shuō)式肝的雁點(diǎn)T堤:當(dāng)α跑村遍畜區(qū)糞間[紛0塘,聽(tīng)1紀(jì)]時(shí),相均應(yīng)獨(dú)的六點(diǎn)T的召集累合欣就毫構(gòu)啄成跑點(diǎn)X與Y之錘間芬的杰連大線購(gòu)。7堂/遼2肆0來(lái)/花2料0貴2曬31群32舟.凸生集:一慌個(gè)慨由n維撈點(diǎn)貫所蟻構(gòu)寒成瘋的允集專合K，疫如針果乳對(duì)雜于K中攪任來(lái)意羅兩燒點(diǎn)X俗,易Y?！实諯，耕恒矛有:則n維互點(diǎn)素集K稱救為格凸禽集宴，弄即K中牛任策意收兩造點(diǎn)逝的躁連崇線惜上投的湯點(diǎn)糟也鼓在K中贈(zèng)。3穿.凸亞組敗合:假康定談?dòng)衚個(gè)n維E握u攀c硬l祥i摩d空加間燙的賴點(diǎn)它磨們級(jí)的小凸俊組己合拒是抗指礙如恢下昏形怠式衡的純點(diǎn)X染:特混別宋，懷兩騙個(gè)饒點(diǎn)X與Y的斥凸葬組餐合福，困叫鬧做要它雖們尋連穿線魂上噸的魯點(diǎn)絨。二帶、圓重障要遭定地理避與行引族理7非/恒2囑0狼/栗2存0扒2示31蛛44嶼.頂世點(diǎn):設(shè)K是燥凸氣集圓，舒點(diǎn)X惠∈衰K；企若是對(duì)K中膜任車何薯兩績(jī)個(gè)酬不揪同畜的根點(diǎn)X灰,察Y，假以錦下痛等肢式恒彩不成蠅立:就籃稱X為借凸憂集K的小頂澆點(diǎn)原?？虛Q齡句吊話鋒說(shuō)籃，罷凸右集初的伴頂川點(diǎn)器，性就動(dòng)是錦不揮在盲凸立集岸中瓜任混意雹兩癥點(diǎn)禮連疼線扛上爸的孔點(diǎn)耗。二昨、寒重杯要泄定售理沿與搭引撤理7烤/割2勇0口/父2劃0是2翠31繪5定爬理1士.若L樹(shù)P問(wèn)乏題付的策可嶄行遣域慢非積空,則剃可嘩行酸域扔為墾凸伙集定煮理2盤.來(lái)L特P問(wèn)放題夫的祝基贈(zèng)可沫行悠解X對(duì)憂應(yīng)L持P問(wèn)奴題喇可水行贏域鞋的忌頂暑點(diǎn)定君理3辛.若L澤P問(wèn)誓題轎有咱最團(tuán)優(yōu)鑰解料，努則幻玉一猴定壁存疊在百至關(guān)少炕一順個(gè)天基烘可店行武解果為怕最怎優(yōu)菜解二饑、陳重萍要丙定承理溜與寒引千理L嘩P問(wèn)臺(tái)題竊的齡標(biāo)貫準(zhǔn)腳型杯，貞見(jiàn)P蔽2還07隨/翠2針0灣/零2嬸0腥2宋31偏6(足1喜)列怪初仗始單紡純?nèi)缧晤w表三餡、單乖純寬形交法兄的饒計(jì)賊算戰(zhàn)步功驟cjc1…cm…cj…cnCB基bx1…xm…xj…xnc1x1b110…aij…a1nc2x2b200…a2j…a2n...............cmxmbm01…amj…amnб=cj-zj0007勇/忠2箭0陸/矩2貞0抹2處31億7(釣2縮慧)從辜一扎個(gè)殃基朱可潛行秀解植轉(zhuǎn)獵換禁為聞相護(hù)鄰領(lǐng)的統(tǒng)另恭一鎮(zhèn)個(gè)垂基吃可轎行既解不冠失旅一找般喘性物，設(shè)初爽始基將可澡行億解量中舟的甘前m個(gè)狐為肯基催變膏量頑，設(shè)輕單坐位嚷矩吃陣敏的壘列鈴向驅(qū)量寒為Pi，安增投廣古矩奶陣拒中轉(zhuǎn)單寧位棒矩爪陣氏以蒸外犬的某暫個(gè)列繞向爺量泰為Pj，中則Pj可寺以火成畝為Pi的慢線偷性販表榆達(dá)解：111a1j.amj三天、單萄純窩形卵法瓣的慨計(jì)田算洲步梅驟7爺/顫2完0是/戀2旗0磨2慚31萄8兩權(quán)式桌相努加室：三縮慧、單備純呆形睬法變的躬計(jì)換算虜步界驟對(duì)陷于鈴一僑個(gè)掘正坑數(shù)閃：θ7灣/概2賓0李/接2垃0牌2暑31抗9除添了X勉(區(qū)0蹈)，虧還吼有卻其運(yùn)他餅解咬嗎露？111a1j.amj只遇需廁：?jiǎn)栒{(diào)題教：X洋(討1稻)是首基哀可晨行諷解嗚嗎順？三駁、單霉純殃形午法提的重計(jì)晚算杏步倦驟7千/惱2艷0忠/娘2勝0繭2峽32脆0要?jiǎng)∈筙穩(wěn)(哄1澤)成敞為覺(jué)基沿可政行簽解指，誕必徑須冊(cè)滿爬足訴：且響，殼至煮少畫一蠶個(gè)業(yè)等書式瞞成范立唯！顯待然建，溫對(duì)動(dòng)于吼小費(fèi)于荒等拜于0的ai芬j，瓶上挪述叢不潔等滔式希無(wú)錯(cuò)條愿件作成然立渠；余對(duì)走于逝大島于0的ai陡j，扮則瓶令兩：三佩、單棋純岸形挎法名的瓣計(jì)傲算就步認(rèn)驟7安/徒2惡0蛋/褲2副0啄2晴32腦1111a1j.amj111以讓上粘的最系疊數(shù)酬矩這陣殊的章初攤等寶行年變吉換執(zhí)，低成碗為換說(shuō)基變替換脂；儉如尿果僅能且變畏換一擁個(gè)基諸變療量郊，側(cè)稱鴨對(duì)舌應(yīng)暑的敗兩催個(gè)售基亂可冒行宜解之為相嶄鄰的盯基奴可臣行撈解供。獄對(duì)喊應(yīng)壘的鐵頂染點(diǎn)后稱拳為相延鄰的俯頂裁點(diǎn)待，賭簡(jiǎn)府稱鄰激點(diǎn)。三巷、單診純后形鄉(xiāng)豐法亂的丸計(jì)率算疫步陰驟7汪/總2慘0碧/際2鑒0肢2雄32映2將X撓(廣0脊)含,奮X累(碎1奪)分察別鵝代騙入棕目帝標(biāo)算函塊數(shù)界：(瓣3扶)最湖優(yōu)辭性晝判陜斷三邀、單稈純岔形況法鄉(xiāng)豐的茅計(jì)趟算哨步派驟7貢/膚2肯0嚼/挽2錯(cuò)0杏2盟32拌3其中：稱為檢驗(yàn)數(shù)，也可表達(dá)為：或：三潑、單矮純算形無(wú)法敢的扒計(jì)供算悅步射驟7廣/脊2少0都/般2略0耐2再32輸4【例】用暢單德純輝型蜂法違解清下浙列L鍵P問(wèn)備題姿：用冠矩寫陣核形姑式曠表頓示撥為誤：四抓、嫩應(yīng)村用閘舉賢例7撿/煩2更0憂/鴨2完0堪2都32昆5首拜先鳥構(gòu)綁造數(shù)初罰始熔單瞇純漫型罰表抵如爬下杜：cj21000CB基bx1x2x3x4x50x315051000x424620100x5511001cj-zj20001四眼、以應(yīng)仁用收舉況例7捏/乳2敏0憑/返2糞0剃2罰32交6cj21000CB基bx1x2x3x4x50x315051000x424620100x5511001cj-zj20001x1四羨、蓋應(yīng)莊用逝舉售例7率/挽2京0顯/稱2蛙0卵2引32調(diào)7cj21000CB基bx1x2x3x4x50x315051002x124620100x5511001cj-zj20001x1四當(dāng)、態(tài)應(yīng)壘用堆舉皂例7濕/寺2左0逼/端2借0完2舞32暗8cj21000CB基bx1x2x3x4x50x315051002x1412/601/600x5104/60-1/61cj-zj000-約1爹/不31秧/摸3第擾一棍次百迭窮代捎結(jié)晴束四倒、及應(yīng)罷用四舉軋例7媽/遠(yuǎn)2底0該/便2痕0透2至32茅9cj21000CB基bx1x2x3x4x50x315051002x1412/601/600x5104/60-1/61cj-zj000-帖1五/云31鼻/丈3x2四鈴、近應(yīng)級(jí)用穗舉謊例7糞/欲2挪0勒/源2球0鵲2錫33懲0cj21000CB基bx1x2x3x4x50x315/20015/4-15/22x17/21001/4-1/21x23/2010-1/43/2cj-zj-巨1攤/榆2-衛(wèi)1惜/采4000四遣、五應(yīng)悲用絕舉堵例7躲/倘2救0襪/解2村0摸2針33停1化脖為古標(biāo)跌準(zhǔn)爛形應(yīng)式撞：五工、設(shè)單泥純餡型沾法俘的濾進(jìn)健一嬌步婆討爺論—人振工某變殿量猜法(大M法)【例】用懲單腿純遷型諒法席求代解恢下督列L父P問(wèn)犬題痕：7眾/赤2偉0帆/持2誕0布2菠33肌2構(gòu)暢造碼初被始賓單蜻純尺型刊表晴：cj-30100-M-MCB基bx1x2x3x4x5x6x70x441111000-Mx61-21-10-110-Mx790310001cj-zj-脹3簽-筐2只M0004喪M-行M1五催、柿單懂純相型搏法蓮的法進(jìn)茄一擊步蔬討連論—人炭工予變雖量定法(大M法)7盯/涂2黑0常/算2若0麥2幟33什3第1次擴(kuò)迭屋代屯：cj-30100-M-MCB基bx1x2x3x4x5x6x70x4330211-100x21-21-10-110-Mx7660403-31cj-zj-未3園+乞6桿M-園4屢M0003槳M1里+直4句M五疤、花單醉純蓮型棉法佳的違進(jìn)畝一非步牙討東論—人虜工留變瞎量遺法(大M法)7瞧/姻2眾0析/拖2車0蓄2香33膜4第2次疑迭丈代際：cj-30100-M-MCB基bx1x2x3x4x5x6x70x400001-1/21/2-1/20x23011/30001/3-3x11102/301/2-1/21/6cj-zj-瓦M(jìn)仁-李3道/禍2-皆M秧+材1功/價(jià)20003像/愈23五脖、息單狐純妖型齡法煌的袋進(jìn)植一任步梁討械論—人速工項(xiàng)變趙量醒法(大M法)7伙/鐵2木0厚/慮2封0桂2煩33搏5第3次萄迭芒代糞：cj-30100-M-MCB基bx1x2x3x4x5x6x70x400001-1/21/2-1/20x25/2-1/2100-1/41/41/41x33/23/20103/4-3/41/4cj-zj-甜M頂+商3闖/斃4-釋M途+熟1氏/慨4-餐9膽/心2-萄3值/范4000五脈、即單粉純擾型概法有的駛進(jìn)育一筆步漿討婚論—人墾工惑變籍量彈法(大M法)7宴/膛2難0完/逃2繩0誼2志33守6同沃樣帽題蹤蝶目六伶、逼單楚純乖型蕩法核的牧進(jìn)朋一拐步陽(yáng)討券論—兩欲階臭段逃法為半了稠保運(yùn)證兩人校工筆變膽量父為0，癢可趣講消目見(jiàn)標(biāo)嫂函倍數(shù)招設(shè)筋為猶：7勢(shì)/歡2識(shí)0籍/屆2魄0臺(tái)2裙33游7構(gòu)涌造妄初毅始艱單夜純未型蘋表湖：cj00000-1-1CB基bx1x2x3x4x5x6x70x441111000-1x61-21-10-110-1x790310001cj-zj-每20004-幫11六算、蹈單冤純餃型紡法屠的溫進(jìn)芹一倆步縣討炒論—兩哈階崇段達(dá)法7那/棍2財(cái)0肌/骨2懷0括2孝33惰8第1次盈迭翠代譽(yù)：cj00000-1-1CB基bx1x2x3x4x5x6x70x4330211-100x21-21-10-110-1x7660403-31cj-zj6-斧400034六偷、任單害純嘴型滋法糕的襲進(jìn)柔一辛步埋討倉(cāng)論—兩床階字段乳法7排/財(cái)2雪0冬/痕2殖0卸2頭33睡9第2次水迭栗代英：cj00000-1-1CB基bx1x2x3x4x5x6x70x400001-1/21/2-1/20x23011/30001/30x11102/301/2-1/21/6cj-zj-蟻1-波100000即麻，泡當(dāng)X(判1劇)=屈(脂1蜂,轎3陳,責(zé)0遭,圈0價(jià),數(shù)0擦,紋0場(chǎng),奴0銷)時(shí)佩，者可托使榨目談標(biāo)綢函兆數(shù)x6+橫x7取侵得地最臨小杏，用當(dāng)x6=服x7=排0時(shí)六撥、嘉單切純懼型兩法達(dá)的晌進(jìn)耐一痰步躁討野論—兩克階候段架法7掠/崗2飾0志/花2差0姓2閱34困0上狗述盯取箭得傷最鬧優(yōu)鑼的慌單家純處型衡迭悔代度中賠止伶的頁(yè)表缸，級(jí)等貨價(jià)敘于碌一例個(gè)侄約逐束公方糟程占組I：而簡(jiǎn)約口束禍方貍程述組I又勞等落價(jià)麗于豬約慢束梳方音程黃組I解I：故螺，粥構(gòu)禮造揭新太的萌初涼始久單拳純肌型作表嚷如耐下盒：六塊、清單鞏純珍型瞞法莖的逗進(jìn)節(jié)一攏步賽討船論—兩削階燒段助法7歐/乘2索0造/潮2清0劫2角34決1cj-30100CB基bx1x2x3x4x50x400001-1/20x23011/300-3x11102/301/2cj-zj六溪、礙單冒純圾型件法室的易進(jìn)溪一艘步盜討城論—兩螺階尊段佳法7睛/賤2縫0霉/秀2挺0鬼2借34牢2cj-30100CB基bx1x2x3x4x50x400001-1/20x23011/300-3x11102/301/2cj-zj第1次他迭銜代嘩：0003兇/融23六擇、滴單絡(luò)純氧型困法劈燕的渾進(jìn)逢一療步寧討覽論—兩秩階腸段豬法7頃/廳2非0資/軟2賽0老2性34清3cj-30100CB基bx1x2x3x4x50x400001-1/20x25/2-1/2100-1/41x33/23/20103/4cj-zj第1次桂迭桑代時(shí)：-搶9速/案2-說(shuō)3承/辦4000六辰、欄單呈純牙型挖法竄的虛進(jìn)次一襲步廣討半論—兩漁階隱段賢法7曾/拼2津0弊/送2抓0道2術(shù)34購(gòu)4七戚、緒單嗚純哨型派法霧解謹(jǐn)?shù)南朴懸闭撗a(bǔ)射充后定姨理1供.如姑果鮮L功P箱問(wèn)借題兩有襪最形優(yōu)黨解光，防則基加可練行盼解中誦必拖有警最伴優(yōu)陪解利。補(bǔ)己充公定斧理2孤.若X(向1攀),劇X(汪2別),位.買.況.房誠(chéng),爪X(貴K譽(yù))皆諸為憶某L袖P問(wèn)城題壩的最室優(yōu)慨解，驚那贏么效它貨們酬的抖凸賤組燒合也割是緒該桌L進(jìn)P恭問(wèn)霉題哄的腸最話優(yōu)斜解置。補(bǔ)失充濱定挑理3沈.若L炕P問(wèn)挨題反的妨可貿(mào)行腫域有雙界，賽而西它蛙的基經(jīng)可殃行芒解中蘋的遇所延有祥最盆優(yōu)慨解撫為心:X(那1悲),橡X(木2銷),等.貝.露.道,康X(督K似),那暫么睜它欄們傾的舅所霞有潮凸衣組玻合跑包論括懼了源該L怎P問(wèn)氧題魚的望所有輩最蓮優(yōu)抖解割。(證維明霉略)以宣下田給六出喜三越個(gè)燭補(bǔ)申充陷定們理匙，博可猶看廳作使是謹(jǐn)求固解競(jìng)線惑性店規(guī)侍劃懼問(wèn)映題潔的鐵基獅本阻依景據(jù)運(yùn)。7齡/芽2河0惡/環(huán)2炸0村2腿34亮5情治況1榆:唯惱一檔最偶優(yōu)稼解只國(guó)需非響基槽變醫(yī)量的趙檢惜驗(yàn)肯數(shù)膨全撫為榴負(fù)柏，域且基內(nèi)變江量中不妙含人鋒工市變炸量，狗該沫解油即泰為唯鞠一最寒優(yōu)版解醋。情仙況2擁:無(wú)妖解1賺.當(dāng)非孫基尖變惡量的研檢攔驗(yàn)魯數(shù)兼全朝為鍵負(fù)脅，雖且基格變險(xiǎn)量中含夢(mèng)有人復(fù)工深變妻量，鉆則畜該L魄P問(wèn)免題掩無(wú)繁解統(tǒng)。2振.可冷行嗽域湊為