4.10 How to make Standard Form (Big M Method) Artificial variables
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1 . Ho to k Stdrd For (ig M Mthod) i.t. Artifiil vribl E vribl Equlity if Ho olv? ut rtifiil vribl hould b ro i th optil olutio.
2 . To-Ph Sipl Mthod Ph I LP i.t. N Ro *liit rtifiil vribl fro Ro Ph II LP Eliit olu of rtifiil vribl fro optil tblu of ph I d otiu ipl thod
3 / -/ / - / -/ / -/ -/ - - Ro / / -/ Ro rh Optil Tblu of Ph I Iitil Tblu of Ph I - / / - Ro - - Ro rh / -/ / / / / -/ / 7 / -/ / / / - / / / Ro - - Ro rh Nt Tblu of Ph I Iitil Tblu of Ph II / -/ / -/ -/ Ro rh
4 . Urtritd-i-Sig Vribl (ur) ur.t..t. - Z - - rh Iitil Tblu Z 7 rh Optil Tblu ly oppoit ig
5 6. Grphil Itrodutio to Sitivity Alyi () A lop = - 6 ().t. - = + () () () D ioprofit li lop = - / C () lop = - 6
6 () A Right-hd id hg = +.t. () () - () () = = =6 6 D () Shdo pri () d 6 ( ) (6 ) C Shdo pri of otrit () i $ offii t of 6
7 6. Iportt Forul )... ( i b b b i.t t. N N otrit - hd id of right olu vtor of : i otrit : olu for th vribl th olu for N tri of ( : th olu for tri of : th obtiv futio offii t ro vtor of ) ( : th obtiv futio offii t ro vtor of : b ) N N Dfiitio
8 Stdrd For.t. N N N N N b Ro of Optil Tblu +) ( Coffiit N N Cotrit of Optil Tblu N b N N N ) N N b b N of i th optiltblu ro : olu of C Coffiit of ( ) d i th optil tblu ro ith lt of Right -hd id of b b olu right i i i - ( ith lt of optil tblu ro for -hd id of ) i optil tblu otrit optil tblu otrit Drivtio ot b y.
9 Epl.t. 6 6 optil vlu = rh of optil tblu ro 6 b = of optil olutio = b rh of optil tblu = olu of i th optil tblu otrit [ ] = Optil Tblu 6 b=.. =. =. b offiit of i th optil tblu ro offiit of i th optil tblu ro....
10 6. Sitivity Alyi t Iitil Tblu Optil Tblu... N Prtr Chg. Obtiv futio offiit of N. Obtiv futio offiit of. Right-hd id of otrit. Colu of N. Add vribl or tivity
11 . Chgig obtiv futio offiit of obi vribl Suppo i hgd to if if ri optil o logr optil If ri optil ftr hg i obi vribl obtiv futio offiit th vlu of th diio vribl d th optil vlu ri uhgd. If ill o logr b optil thi i ot optil olutio (uboptil). Th rdud ot for obi vribl i th iu out by hih th vribl obtiv futio offiit b ird bfor th urrt bi bo uboptil d it bo optil for th obi vribl to tr th bi.
12 . Chgig obtiv futio offiit of bi vribl Suppo Vlu of th diio vribl do ot hg but -vlu do hgd. If 7 ht i? - -. Coffiit of h obi vribl i i th optil tblu ro i hgd 6 to6. Rg of vlu o for hih urrt bi ri / optil If y vribl i ro h gtiv offiit th urrt bi i o logr optil. If.. tob. 7 Prod ipl d fid th optil tblu. Tbl i p.6.
13 . Chgig th right-hd id of otrit Suppo b b i hgd to. Currt bi ri optil 6 b If th right-hd id of h otrit i th tblu ri ogtiv th urrt bi ri optil. If th right-hd id of y otrit i gtiv th urrt bi i ifibl. Chg of vlu of optil olutio (-vlu) d th vlu of vlu of ( b) vlu of ( b) C of urrt bi ri optil Vlu of Z (Optil Vlu) C of Ob.Fu. N Not Chg Not Chg C of Ob.Fu. Not Chg Chg rh of otrit Chg Chg
14 . Chgig th olu of obi vribl If th olu of obi vribl i hgd th urrt bi ri optil. th urrt bi i o logr optil if if Pri Out: Clult th offiit of i th optil tblu ro. Addig tivity Additio of th olu ( diio vribl) th urrt bi ri optil. th urrt bi i o logr optil if if
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