นตอนว, มเพล, กซ, บทความน, งหมดหร, อบางส, วน, เน, อหา, ปแบบ, หร, อล, กษณะการนำเสนอท, ไม, เหมาะสมสำหร, บสาราน, กรม, โปรดอภ, ปรายป, ญหาด, งกล, าวในหน, าอภ, ปราย, หากบทความน, เข, าก, นได, บโครงการพ, อง, โปรดทำการแจ, งย, ายแทนบทความน, ได, บแจ, งให, ปร, บปร, งหลายข,. bthkhwamnithnghmdhruxbangswn mienuxha rupaebb hruxlksnakarnaesnxthiimehmaasmsahrbsaranukrm oprdxphipraypyhadngklawinhnaxphipray hakbthkhwamniekhaknidkbokhrngkarphinxng oprdthakaraecngyayaethnbthkhwamniidrbaecngihprbprunghlaykhx krunachwyprbprungbthkhwam hruxxphipraypyhathihnaxphipray bthkhwamnitxngkarcdrupaebbkhxkhwam karcdhna karaebnghwkhx karcdlingkphayin aelaxun bthkhwamniyngkhadaehlngxangxingephuxphisucnkhwamthuktxng bthkhwamnitxngkarsrupenuxhabthkhwamiwinyxhnaaerksudkhntxnwithisimephlks xngkvs simplex algorithm hrux withisimephlks xngkvs simplex method caxasyhlkkarkhxngemthriksekhachwyinkarhaphllphththiehmaasmthisud sungcathaihehnthungkarepliynaeplngkhxngtwaeprinaetlakhntxnxyangmiehtuphl 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sungrupmatrthancaxyuinrupkhathimakthisudkhxng Z c 1 x 1 c 2 x 2 c n x n displaystyle Z c 1 x 1 c 2 x 2 cdots c n x n phayitenguxnikh a 11 x 1 a 12 x 2 a 1 n x n b 1 a 21 x 1 a 22 x 2 a 2 n x n b 2 a n 1 x 1 a n 2 x 2 a n n x n b n x 1 0 x 2 0 x n 0 displaystyle begin aligned a 11 x 1 a 12 x 2 cdots a 1n x n amp leq b 1 a 21 x 1 a 22 x 2 cdots a 2n x n amp leq b 2 amp vdots a n1 x 1 a n2 x 2 cdots a nn x n amp leq b n x 1 geq 0 x 2 geq 0 ldots x n amp geq 0 end aligned cakrupaebbomedlkhnitsastrkhxngopraekrmechingesnkhathimakthisudkhxng Z c 1 x 1 c 2 x 2 c 3 x 3 displaystyle Z c 1 x 1 c 2 x 2 c 3 x 3 phayitenguxnikh a 11 x 1 a 12 x 2 a 13 x 3 b 1 a 21 x 1 a 22 x 2 a 23 x 3 b 2 a 31 x 1 a 32 x 2 a 33 x 3 b 3 x 1 0 x 2 0 x 3 0 displaystyle begin aligned a 11 x 1 a 12 x 2 a 13 x 3 amp leq b 1 a 21 x 1 a 22 x 2 a 23 x 3 amp leq b 2 a 31 x 1 a 32 x 2 a 33 x 3 amp leq b 3 x 1 geq 0 x 2 geq 0 x 3 amp geq 0 end aligned ekhiynsmkarephuxephimetimtwaeprchwy iddngni Z c 1 x 1 c 2 x 2 c 3 x 3 0 a 11 x 1 a 12 x 2 a 13 x 3 x 4 b 1 a 21 x 1 a 22 x 2 a 23 x 3 x 5 b 2 a 31 x 1 a 32 x 2 a 33 x 3 x 6 b 3 x 1 0 x 2 0 x 3 0 x 4 0 x 5 0 x 6 0 displaystyle begin aligned Z c 1 x 1 c 2 x 2 c 3 x 3 amp 0 a 11 x 1 a 12 x 2 a 13 x 3 x 4 amp leq b 1 a 21 x 1 a 22 x 2 a 23 x 3 x 5 amp leq b 2 a 31 x 1 a 32 x 2 a 33 x 3 x 6 amp leq b 3 x 1 geq 0 x 2 geq 0 x 3 geq 0 x 4 geq 0 x 5 geq 0 x 6 amp geq 0 end aligned twaeprthiephimekhama aekikh twaepraebb Slackinxsmkarthimi displaystyle leq odythangsayepnkardaeninkarkhxngtwaepr aelathangkhwaepnkhatwelkhtwhnung erasamarthephimtwaepraebb Slack ekhaipthangsayidephuxepntwaethnephimkhaihethakbkhathangkhwa echncakkhxcakd 7 x 1 34 x 2 125 displaystyle 7x 1 34x 2 leq 125 samarthekhiynepn 7 x 1 34 x 2 x 3 125 displaystyle 7x 1 34x 2 x 3 125 emux x 3 0 displaystyle x 3 geq 0 twaepraebb Surplusinxsmkarthimi displaystyle geq odythangsayepnkardaeninkarkhxngtwaepr aelathangkhwaepnkhatwelkhtwhnung erasamarthephimtwaepraebb Surplus 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0 0 displaystyle 0 b 1 displaystyle b 1 x 5 displaystyle x 5 0 displaystyle 0 a 21 displaystyle a 21 a 22 displaystyle a 22 a 23 displaystyle a 23 0 displaystyle 0 1 displaystyle 1 0 displaystyle 0 b 2 displaystyle b 2 x 6 displaystyle x 6 0 displaystyle 0 a 31 displaystyle a 31 a 32 displaystyle a 32 a 33 displaystyle a 33 0 displaystyle 0 0 displaystyle 0 1 displaystyle 1 b 3 displaystyle b 3 dd dd dd 3 eluxktwaeprkhaekha entering variable khuxkareluxktwaeprthiimepntwaeprmulthan non basic variable ihepntwaeprmulthan basic variable odyducaksmprasiththikhxngtwaeprinsmkarepahmay aethw Z thitidlbmakthisud aetthasmprasiththikhxngtwaeprthuktwepnbwkhruxsunyaelw aesdngwathungcudthiehmaasm optimal solution imtxngthatxipxik4 eluxktwaeprkhaxxk leaving variable dwykarhaxtraswnkhxngkhaphllphthkbsmprasiththikhxngtwaeprekhathieluxkiwinkhnthi 3 imtxngkhanungthungsmprasiththithiepnlbhruxsuny eluxkxtraswntasudkhxngtwaeprmulthan xyuthitwidaesdngwatwnncaepntwaeprxxk5 epliyntwaeprmulthan 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displaystyle 2 3 displaystyle 3 1 displaystyle 1 0 displaystyle 0 100 displaystyle 100 x 4 displaystyle x 4 0 displaystyle 0 4 displaystyle 4 2 displaystyle 2 0 displaystyle 0 1 displaystyle 1 120 displaystyle 120 phicarnaaethwaerk Z displaystyle Z khasmprasiththithimikhanxysud khux 6 displaystyle 6 cungeluxk x 1 displaystyle x 1 epntwaeprkhaekha caknnphicarnaxtraswnkhxngkha b displaystyle b kbsmprasiththikhxngtwaeprkhaekha caidwa aethwthi x 3 displaystyle x 3 mixtraswnepn 100 2 50 displaystyle frac 100 2 50 aelaaethwthi x 4 displaystyle x 4 mixtraswnepn 120 4 30 displaystyle frac 120 4 30 dngnncungeluxk x 4 displaystyle x 4 epntwaeprkhaxxkepliynih x 1 displaystyle x 1 epntwaeprmulthan odyaelkthikb x 4 displaystyle x 4 dwywithikardaeninkartamaethw caidtarangsimephlks dngni R 3 1 4 R 3 R 2 2 R 3 R 2 R 1 6 R 3 R 1 displaystyle begin aligned R 3 amp frac 1 4 R 3 R 2 amp 2R 3 R 2 R 1 amp 6R 3 R 1 end aligned Z displaystyle Z x 1 displaystyle x 1 x 2 displaystyle x 2 x 3 displaystyle x 3 x 4 displaystyle x 4 b displaystyle b Z displaystyle Z 1 displaystyle 1 0 displaystyle 0 1 displaystyle 1 0 displaystyle 0 3 2 displaystyle frac 3 2 180 displaystyle 180 x 3 displaystyle x 3 0 displaystyle 0 0 displaystyle 0 2 displaystyle 2 1 displaystyle 1 1 2 displaystyle frac 1 2 40 displaystyle 40 x 1 displaystyle x 1 0 displaystyle 0 1 displaystyle 1 1 2 displaystyle frac 1 2 0 displaystyle 0 1 4 displaystyle frac 1 4 30 displaystyle 30 phicarnaaethwaerk Z displaystyle Z khasmprasiththithimikhanxysud khux 1 displaystyle 1 cungeluxk x 2 displaystyle x 2 epntwaeprkhaekha caknnphicarnaxtraswnkhxngkha b displaystyle b kbsmprasiththikhxngtwaeprkhaekha caidwa aethwthi x 3 displaystyle x 3 mixtraswnepn 40 2 20 displaystyle frac 40 2 20 aelaaethwthi x 1 displaystyle x 1 mixtraswnepn 30 1 2 60 displaystyle frac 30 1 2 60 dngnncungeluxk x 3 displaystyle x 3 epntwaeprkhaxxkepliynih x 2 displaystyle x 2 epntwaeprmulthan odyaelkthikb x 3 displaystyle x 3 dwywithikardaeninkartamaethw caidtarangsimephlks dngni R 2 1 2 R 2 R 3 1 2 R 2 R 3 R 1 R 2 R 1 displaystyle begin aligned R 2 amp frac 1 2 R 2 R 3 amp frac 1 2 R 2 R 3 R 1 amp R 2 R 1 end aligned Z displaystyle Z x 1 displaystyle x 1 x 2 displaystyle x 2 x 3 displaystyle x 3 x 4 displaystyle x 4 b displaystyle b Z displaystyle Z 1 displaystyle 1 0 displaystyle 0 0 displaystyle 0 1 2 displaystyle frac 1 2 5 4 displaystyle frac 5 4 200 displaystyle 200 x 2 displaystyle x 2 0 displaystyle 0 0 displaystyle 0 1 displaystyle 1 1 2 displaystyle frac 1 2 1 4 displaystyle frac 1 4 20 displaystyle 20 x 1 displaystyle x 1 0 displaystyle 0 1 displaystyle 1 0 displaystyle 0 1 4 displaystyle frac 1 4 3 8 displaystyle frac 3 8 20 displaystyle 20 emuxphicarnatarangsimephlkskcaehnwa smprasiththiinsmkarepahmay phicarnaaethw Z mikhaimtidlbthnghmd dngnnerakidphlechlythiehmaasmthisudaelwdngnix 1 20 x 2 20 displaystyle x 1 20 x 2 20 khamakthisudkhxng Z 200 displaystyle Z 200 prasiththiphaph aekikhkhntxnwithisimephlks 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