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0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times New Roman CE" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Output" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 32 "Z\341klady matematick\351 optimalizace" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 257 " " 0 "" {TEXT -1 34 "1. \332vod - z\341kladn\355 pojmy, bal\355k \"" } {TEXT 333 7 "simplex" }{TEXT 334 1 "\"" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 " \330e\232en\355 \372loh line\341rn\355ho programov \341n\355 n\341m usnad\362uje pr\341ce s knihovnou " }{TEXT 406 7 "si mplex" }{TEXT 408 1 "." }}{PARA 0 "" 0 "" {TEXT 407 0 "" }{TEXT -1 62 " Sta\350\355 na za\350\341tku v\375po\350tu \"zavolat\" tuto knih ovnu p\370\355kazem" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(simplex):" }}{PARA 7 "" 1 "" {TEXT -1 87 "Warning, the protected names maximize and minimize have been redef ined and unprotected\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 " a \+ d\341le ji\236 m\371\236eme pou\236\355vat spec. funkce v n\355 obsa \236en\351, mezi kter\351 pat\370\355 nap\370." }}{PARA 0 "" 0 "" {TEXT -1 95 " basis convex hull cterm" }}{PARA 0 "" 0 "" {TEXT -1 97 " display maximize \+ minimize" }}{PARA 0 "" 0 "" {TEXT -1 105 " \+ pivot ratio \+ standardize" }}{PARA 0 "" 0 "" {TEXT -1 87 " a \+ \370ada dal\232\355ch. Uveden\351 p\370\355kazy n\341m umo\236\362uj \355 \370e\232it \372lohy line\341rn\355ho programov\341n\355 " }} {PARA 0 "" 0 "" {TEXT -1 95 " komplexn\354 (kdy n\341s zaj\355m \341 pouze v\375sledn\351 optim\341ln\355 \370e\232en\355 a pr\371b \354h v\375po\350tu z\371st\341v\341 skryt)," }}{PARA 0 "" 0 "" {TEXT -1 66 " nebo po d\355l\350\355ch kroc\355ch (hled\341n\355 baze, u r\350en\355 pivota, atd.). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 30 "Vysv\354tlen\355 jednotliv\375ch funkc \355" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 " Uk\341\236eme si nyn\355 mo\236nosti pou\236it\355 jednotliv \375ch p\370\355kaz\371." }}{PARA 0 "" 0 "" {TEXT 476 28 " NONNEGATIV E / UNRESTRICTED" }}{PARA 0 "" 0 "" {TEXT -1 81 " - u prom\354nn\375c h, s nimi\236 pracujeme, m\371\236eme p\370edem zadat omezen\355, zda \+ p\370ipou\232t\355me" }}{PARA 0 "" 0 "" {TEXT -1 85 " pouze nez \341porn\351 hodnoty (co\236 programu sd\354l\355me kl\355\350ov\375m \+ slovem NONNEGATIVE) nebo" }}{PARA 0 "" 0 "" {TEXT -1 81 " zda toto omezen\355 nepo\236adujeme (lze zadat pomoc\355 kl\355\350ov\351ho sl ova UNRESTRICTED)" }}{PARA 0 "" 0 "" {TEXT -1 77 " - konkr\351tn\355 \+ pou\236it\355 t\354chto dvou mo\236nost\355 uvid\355me v n\341sleduj \355c\355ch p\370\355kladech" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 436 30 " Basis (soustava lin. rovnic)" }} {PARA 0 "" 0 "" {TEXT -1 85 " - vyp\355\232e seznam prom\354nn\375ch (z ka\236d\351 rovnice po jedn\351) odpov\355daj\355c\355ch bazi u \236\355van\351 " }}{PARA 0 "" 0 "" {TEXT -1 46 " v p\370\355slu \232n\351m kroku simplexov\351m algoritmu" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 437 7 "Pozor! " }{TEXT -1 71 "Pou\236it\341 soustava li n. rovnic mus\355 b\375t ve tvaru, kter\375 z\355sk\341me p\370\355kaz em " }{TEXT 439 6 "setup " }{TEXT -1 17 "(viz dal\232\355 text)." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "basis ([x1=6+2*x2+3*x3+x4, x 5=-x1+2*x2-3*x3+2, x6=x1+x2+3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7% %#x1G%#x5G%#x6G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 426 46 " Convert (seznam lin. (ne-)rovnic , equality)" }} {PARA 0 "" 0 "" {TEXT -1 59 " - v\232echny nerovnice/rovnice ze sezna mu p\370evede na typ \"=\"" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{TEXT 427 8 " Pozor! " }{TEXT -1 57 "Tato operace v\236dy nezachov\341v\341 \+ mno\236inu p\370\355pustn\375ch \370e\232en\355." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "convert(\{4*x1+5*x2-3*x3<=2, 5*x1-2*x2+x3>=-5 , 3*x1+x2-4*x3=6\}, equality);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/, (*&\"\"$\"\"\"%#x1GF(F(%#x2GF(*&\"\"%F(%#x3GF(!\"\"\"\"'/,(*&F,F(F)F(F (*&\"\"&F(F*F(F(*&F'F(F-F(F.\"\"#/!\"&,(*&F4F(F)F(F(*&F6F(F*F(F.F-F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 434 41 " Convert (seznam lin. (ne-)rovnic , std)" }}{PARA 0 "" 0 "" {TEXT -1 66 " - uprav\355 soustavu podm\355nek do podoby rovnic (kter \351 na rozd\355l od " }{TEXT 435 15 "convert / stdle" }{TEXT -1 34 " \+ nep\370em\354\362uje na dvojice nerovnic) " }}{PARA 0 "" 0 "" {TEXT -1 24 " a nerovnic typu \"<=\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "convert(\{2<=3*x1-2*x2,-2>=4*x1+x2, -5=x1+x2\}, std); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%1,&*&\"\"$\"\"\"%#x1GF(!\"\"*&\" \"#F(%#x2GF(F(!\"#1,&*&\"\"%F(F)F(F(F-F(F./,&F)F*F-F*\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 428 2 " " }}{PARA 0 "" 0 "" {TEXT 429 43 " Con vert (seznam lin. (ne-)rovnic , stdle)" }}{PARA 0 "" 0 "" {TEXT -1 90 " - v\232echny nerovnice/rovnice ze seznamu zap\355\232e v podob\354 \+ nerovnic typu \"<=\", s konstantami" }}{PARA 0 "" 0 "" {TEXT -1 32 " \+ p\370eveden\375mi na pravou stranu" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "convert(\{4*x1+5*x2-3*x3<=2, 5*x1-2*x2+x3>=-5, 3*x1+ x2-4*x3=6\}, stdle); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&1,(*&\"\"%\"\"\"%#x1GF(F(*&\"\"&F(%#x2GF(F(*&\" \"$F(%#x3GF(!\"\"\"\"#1,(*&F+F(F)F(F0*&F1F(F,F(F(F/F0F+1,(*&F.F(F)F(F( F,F(*&F'F(F/F(F0\"\"'1,(*&F.F(F)F(F0F,F0*&F'F(F/F(F(!\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 " Zde si m\371\236eme pov\232imnout, \+ \236e rovnici tento p\370\355kaz zap\355\232e v podob\354 dvou nerovni c. " }}{PARA 0 "" 0 "" {TEXT -1 45 " Pozn. T\351to funkci ekviv alentn\355 je p\370\355kaz " }{TEXT 433 13 "standardize, " }{TEXT -1 7 "viz p\370." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "standardiz e(\{4*x1+5*x2-3*x3<=2, 5*x1-2*x2+x3>=-5, 3*x1+x2-4*x3=6\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&1,(*&\"\"%\"\"\"%#x1GF(F(*&\"\"&F(%#x2GF(F (*&\"\"$F(%#x3GF(!\"\"\"\"#1,(*&F+F(F)F(F0*&F1F(F,F(F(F/F0F+1,(*&F.F(F )F(F(F,F(*&F'F(F/F(F0\"\"'1,(*&F.F(F)F(F0F,F0*&F'F(F/F(F(!\"'" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 412 26 " Convexhull (mno\236ina bod\371)" }}{PARA 0 "" 0 "" {TEXT -1 102 " - program vyp\355\232e vrcholy konvexn\355ho obalu mno \236iny bod\371 uveden\351 v argumentu p\370i vol\341n\355 t\351to pro cedury" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 413 7 " Pozor!" } {TEXT -1 110 " V zad\341n\355 je nutno zad\341vat v\236dy dvojici sou \370adnic pro ka\236d\375 bod, a to v podob\354 \350\355sel (nep\370ip ou\232t\355 se prom\354nn\341)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 83 " P\370. Najd\354te konvexn\355 obal mn o\236iny bod\371 \{[0,0], [1,1], [2,0], [1,0], [1, 1/2]\}." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "convexhull (\{[0,0], [1,1], \+ [2,0], [1,0], [1,1/2]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%7$\"\"! F%7$\"\"#F%7$\"\"\"F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 128 " - v tomto p\370\355pad\354 procedura vybrala ze zadan\375ch bod\371 vrcho ly polyedru, kter\375 je jejich konvexn\355m obalem a zapsala tyto bod y " }}{PARA 0 "" 0 "" {TEXT -1 136 " v po\370ad\355 proti sm\354r u chodu hodinov\375ch ru\350i\350ek ; pod\355vejme se na to, co proved e program v p\370\355pad\354, kdy\236 p\370id\341me bod [sqrt(2), 1/2] :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "convexhull (\{[0,0], [ 1,1], [2,0], [1,0], [1,1/2], [sqrt(2), 1/2]\});" }}{PARA 8 "" 1 "" {TEXT -1 177 "Error, invalid input: convexhull expects its 1st argumen t, ps, to be of type \{set, list\}(list(numeric)), but received \{[0, \+ 0], [1, 1], [2, 0], [1, 0], [1, 1/2], [2^(1/2), 1/2]\}\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 129 " - vid\355me, \236e je nutn\351 zad \341vat jako sou\370adnice u\236 p\370\355mo konkr\351tn\355 hodnoty, \+ nesta\350\355 \350\355slo zapsat nap\370. ve tvaru sqrt(2) apod. " } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 " " }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 409 49 "Cterm (mno\236ina line\341rn\355ch rovnic, resp . nerovnic)" }}{PARA 0 "" 0 "" {TEXT -1 118 " - tato procedura d\341 \+ na v\375stupu v\375\350et konstant, jednu pro ka\236dou ze zadan\375ch rovnic, resp. nerovnic; tyto konstanty " }}{PARA 0 "" 0 "" {TEXT -1 120 " jsou tvo\370eny tak, \236e v\232echny konstanty v r\341mci ka \236d\351 rovnice jsou p\370evedeny na pravou stranu a se\350teny, viz p\370\355klad " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "cterm([2 *x+4*z-5+4*y+8=5, 5*y-3*x+1/2*z-1/2<=0, 3*x-2*y+6>=6]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7%\"\"##\"\"\"F$\"\"!" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 3 " " }{TEXT 414 7 "Pozor! " }{TEXT -1 127 "Nesm\355me uv eden\375 v\375\350et rovnic/ nerovnic zapomenout spr\341vn\354 uz\341v orkovat! Jinak by procedura zpracovala pouze prvn\355 (ne-)rovnici. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 415 44 " Display (mno\236ina line\341rn\355ch (ne-)rovnic) " }}{PARA 0 " " 0 "" {TEXT -1 79 " - procedura zap\355\232e soustavu line\341rn \355ch (ne-)rovnic ve tvaru maticov\351 rovnice" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 71 "with(simplex, display) ([x1+x2+3*x4<=9, x2+(-3 )*x3+6*x4<=9, x1+x3<=4]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#1*&-%'m atrixG6#7%7&\"\"\"F+\"\"$\"\"!7&F-F+\"\"'!\"$7&F+F-F-F+F+-%'MATRIXG6#7 &7#%#x1G7#%#x2G7#%#x4G7#%#x3GF+-F'6#7%7#\"\"*FA7#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 416 6 "Pozor!" }{TEXT -1 62 " \+ Zadan\341 soustava mus\355 b\375t ve tvaru z\355skan\351m aplikac\355 p\370\355kazu " }{TEXT 410 7 "setup, " }{TEXT -1 21 "jinak tato proce dura " }}{PARA 0 "" 0 "" {TEXT -1 132 " nefunguje optim \341ln\354, zkusme nap\370. jej\355 chov\341n\355 v p\370\355pad\354, kdy u p\370edchoz\355ho p\370\355kladu nahrad\355me nerovnosti rovnos tmi:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "with(simplex, displ ay) ([ x1+x2+3*x4=9, x2+(-3)*x3+6*x4=9, x1+x3=4]);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7#/-%'matrixG6#7%7&\"\"\"F*\"\"$\"\"!7&F,F*\"\"'!\"$7 &F*F,F,F*-F&6#7%7#\"\"*F47#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 117 " Vid\355me, \236e procedura \"vynechala\" sloupec t \375kaj\355c\355 se nezn\341m\375ch, co\236 v tomto p\370\355pad\354, \+ kdy Maple prohodil " }{TEXT 477 2 "x3" }{TEXT -1 3 " a " }{TEXT 478 2 "x4" }{TEXT -1 24 ", je v\375razn\375 nedostatek." }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 417 21 " Dual (lin. fun kce " }{TEXT 418 1 "f" }{TEXT 419 49 ", mno\236ina lin. nerovnic, ozn a\350en\355 nov\351 prom\354nn\351 " }{TEXT 420 1 "y" }{TEXT 421 1 ") " }}{PARA 0 "" 0 "" {TEXT -1 33 " - funkce, kter\341 k dan\351 \372 loze " }{TEXT 422 6 "max f " }{TEXT -1 19 "najde \372lohu du\341ln\355 " }{TEXT 425 5 "min g" }{TEXT -1 41 ", p\370i\350em\236 prom\354nn \351 v du\341ln\355 \372loze ozna\350\355 " }}{PARA 0 "" 0 "" {TEXT -1 38 " dle na\232eho po\236adavku y1, y2, ..." }}{PARA 0 "" 0 " " {TEXT 423 11 " Pozor! " }{TEXT -1 85 "Zad\341van\351 line\341rn \355 nerovnice mus\355 b\375t ve spec. tvaru, kter\375 lze z\355skat p omoc\355 p\370\355kazu " }{TEXT 424 15 "convert / stdle" }{TEXT -1 2 " . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 " P\370. Najd\354te du\341ln\355 \372lohu k \372loze \+ max (x1 + 2x2)" }}{PARA 0 "" 0 "" {TEXT -1 76 " \+ -x1 + x2 + x3 <= 1" }}{PARA 0 "" 0 "" {TEXT -1 76 " \+ x1 + 2 x2 - x3 <= 4" }}{PARA 0 "" 0 "" {TEXT -1 75 " \+ 2 x1 - x2 + 3 x3 <= 2" }}{PARA 0 "" 0 "" {TEXT -1 81 " \+ x1, x2, x3 >= 0. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "dual(x1+2*x2, \{-x1 + x2 + x3 <= 1, x1 +2*x2 -x3 <= \+ 4, 2*x1 -x2 +3*x3 <= 2\}, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,(%#y 1G\"\"\"*&\"\"%F%%#y2GF%F%*&\"\"#F%%#y3GF%F%<%1F%,(F$!\"\"F(F%*&F*F%F+ F%F%1F*,(F$F%*&F*F%F(F%F%F+F/1\"\"!,(F$F%F(F/*&\"\"$F%F+F%F%" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 430 52 " \+ Feasible (seznam lin. (ne-)rovnic, typ prom\354nn\351)" }}{PARA 0 " " 0 "" {TEXT -1 124 " - rozhodne, zda existuje n\354jak\351 p\370 \355pustn\351 \370e\232en\355 zadan\351 soustavy lin. (ne-)rovnic (v t om p\370\355pad\354 vr\341t\355 logickou hodnotu " }{TEXT 431 4 "true " }{TEXT -1 2 ") " }}{PARA 0 "" 0 "" {TEXT -1 32 " \350i nikoliv \+ (vr\341t\355 hodnotu " }{TEXT 432 5 "false" }{TEXT -1 2 ") " }}{PARA 0 "" 0 "" {TEXT -1 111 " - druh\375 parametr je nepovinn\375 - lze s pecifikovat, zda po\236adujeme, aby prom\354nn\351 byly nez\341porn \351 nebo neomezen\351" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "f easible(\{2*x1+4*x2>=4, x1+2*x2<=-2\}, NONNEGATIVE);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "feasible(\{2*x1+4*x2>=4, x1+2*x2>=-2\}, NONNEGATIVE);" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }{XPPMATH 20 "6#%%trueG" }}}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 " " }{TEXT 438 58 "Maximize (\372\350elov\341 funkce, seznam lin. podm\355nek, typ pr om.)" }}{PARA 0 "" 0 "" {TEXT -1 95 " - funkce najde hodnoty prom \354nn\375ch, pro n\354\236 nab\375v\341 \372\350elov\341 funkce sv \351 nejv\354t\232\355 mo\236n\351 hodnoty" }}{PARA 0 "" 0 "" {TEXT -1 102 " - na m\355st\354 t\370et\355ho (voliteln\351ho) parametru \+ lze specifikovat, zda uva\236ujeme nez\341porn\351 (NONNEGATIVE)" }} {PARA 0 "" 0 "" {TEXT -1 44 " nebo neomezen\351 (UNRESTRICTED) pr om\354nn\351" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "maximize (x 1+x2,\{4*x2+3*x1<=12, 6*x1+x2<=18\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%#x1G#\"#?\"\"(/%#x2G#\"\"'F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 " V tomto p\370\355pad\354 \372\350elov\341 funkce nab\375v \341 maxim\341ln\355 hodnoty pro " }{TEXT 442 7 "x1=20/7" }{TEXT -1 3 " , " }{TEXT 443 7 "x2= 6/7" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "maximize (x1-x2,\{3*x1+2*x2>=6\}, UNRESTRICTED);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 " V tomto p\370\355pad\354 \+ \372\350elov\341 funkce nen\355 shora omezen\341 (Maple nezap\355\232e \236\341dn\375 v\375sledek). " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "maximize (x1-x2,\{4*x2+2*x1<=12, 2*x1+3*x2<=-6\}, NONNEGATIVE) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 " Pr\341zdnou z\341vorkou n\341m Maple nazna\350il, \+ \236e zadan\341 \372loha nem\341 \236\341dn\351 p\370\355pustn\351 \+ \370e\232en\355." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT 440 62 " Minimize (\372\350elov\341 funkce, seznam lin . podm\355nek, typ prom.)" }}{PARA 0 "" 0 "" {TEXT -1 95 " - funkce najde hodnoty prom\354nn\375ch, pro n\354\236 nab\375v\341 \372\350el ov\341 funkce sv\351 nejmen\232\355 mo\236n\351 hodnoty" }}{PARA 0 "" 0 "" {TEXT -1 32 " (funkce analogick\341 funkci " }{TEXT 441 8 "m aximize" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 102 " - na m \355st\354 t\370et\355ho (voliteln\351ho) parametru lze specifikovat, \+ zda uva\236ujeme nez\341porn\351 (NONNEGATIVE)" }}{PARA 0 "" 0 "" {TEXT -1 44 " nebo neomezen\351 (UNRESTRICTED) prom\354nn\351" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "minimize (x1+x2,\{4*x2+3*x1 <=12, 6*x1+x2<=18\},NONNEGATIVE);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#< $/%#x2G\"\"!/%#x1GF&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 " V tom to p\370\355pad\354 \372\350elov\341 funkce nab\375v\341 minim\341ln \355 hodnoty pro " }{TEXT 444 4 "x1=0" }{TEXT -1 3 " , " }{TEXT 445 5 "x2= 0" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "m inimize (x1-x2,\{3*x1+2*x2>=6\}, UNRESTRICTED);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 " V tomto p\370\355pad\354 \372\350elov\341 funkc e nen\355 zdola omezen\341 (Maple nezap\355\232e \236\341dn\375 v\375s ledek). " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "minimize (x1-x 2,\{4*x2+2*x1<=12, 2*x1+3*x2<=-6\}, NONNEGATIVE);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 " Pr\341 zdnou z\341vorkou n\341m Maple op\354t nazna\350il, \236e zadan\341 \+ \372loha nem\341 \236\341dn\351 p\370\355pustn\351 \370e\232en\355." } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 " \+ " }{TEXT 458 23 "Pivot (soustava rovnic " }{TEXT 473 1 "C" }{TEXT 474 11 ", prom\354nn\341 " }{TEXT 460 1 "x" }{TEXT 461 31 ", rovnice n ebo soustava rovnic)" }}{PARA 0 "" 0 "" {TEXT -1 110 " - tato funk ce sestav\355 novou soustavu rovnic a to tak, \236e z nab\355dnut\351 \+ rovnice ve t\370et\355m parametru vyj\341d\370\355 " }}{PARA 0 "" 0 " " {TEXT -1 18 " prom\354nnou " }{TEXT 459 3 "x, " }{TEXT -1 40 "a toto vyj\341d\370en\355 dosad\355 do cel\351 soustavy" }{TEXT 462 1 " " }{TEXT -1 32 "(p\370echod od jedn\351 baze ke druh\351)" }} {PARA 0 "" 0 "" {TEXT 471 13 " Pozor! " }{TEXT -1 43 "Syst\351m C mus\355 b\375t v podob\354 z\355skan\351 p\370\355kazem" }{TEXT 472 7 " setup." }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "pivot(\{_SL1=2-x2-x3+2*x4,x1=3-x2-2*x3-3*x4\},x2,_SL1=2-x2-x3+2*x4 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%#x2G,*%%_SL1G!\"\"\"\"#\"\" \"%#x3GF(*&F)F*%#x4GF*F*/%#x1G,*F*F*F'F*F+F(*&\"\"&F*F-F*F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 463 4 " " }}{PARA 0 "" 0 "" {TEXT 479 30 " Pivoteqn (soustava rovnic " }{TEXT 469 1 "C" }{TEXT 470 11 ", \+ prom\354nn\341 " }{TEXT 464 1 "x" }{TEXT 465 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 108 " - tato funkce vybere ze soustavy rovnic tu (resp. t y), pro kter\351 je minim\341ln\355 hodnota pod\355lu (vzhledem " }} {PARA 0 "" 0 "" {TEXT -1 18 " k prom\354nn\351 " }{TEXT 466 1 "x " }{TEXT -1 45 "), dle n\354ho\236 vyb\355r\341me novou prom\354nnou d o baze" }}{PARA 0 "" 0 "" {TEXT -1 70 " - v p\370\355pad\354, kdy \+ \236\341dn\375 z uva\236ovan\375ch pod\355l\371 nen\355 kladn\375, zah l\341s\355 " }{TEXT 475 5 "FAIL " }}{PARA 0 "" 0 "" {TEXT -1 5 " \+ " }{TEXT 467 7 "Pozor! " }{TEXT -1 43 "Syst\351m C mus\355 b\375t v po dob\354 z\355skan\351 p\370\355kazem" }{TEXT 468 7 " setup." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "pivoteqn(\{_SL1=2-x2-x3+2*x4 ,x1=3-x2-2*x3-3*x4\},x2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#/%%_SL1 G,*\"\"#\"\"\"%#x2G!\"\"%#x3GF**&F'F(%#x4GF(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 55 "pivoteqn(\{_SL2=8+2*x2+x3+8*x4,x1=3+4*x2-2*x3- 3*x4\},x2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%FAILG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 " \+ " }{TEXT 454 41 "Pivotvar (\372\350elov\341 funkce, po\370ad\355 pr om. - " }{TEXT -1 18 "voliteln\375 parametr" }{TEXT 457 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 110 " - jestli\236e \372\350elovou funkci zap \355\232eme pouze pomoc\355 nebazick\375ch prom\354nn\375ch, tento p \370\355kaz n\341m ur\350\355 prom\354nnou" }}{PARA 0 "" 0 "" {TEXT -1 79 " s kladnou relativn\355 cenou, kterou lze p\370idat do no v\354 konstruovan\351 baze " }}{PARA 0 "" 0 "" {TEXT -1 112 " - p okud up\370ednost\362ujeme n\354jak\351 po\370ad\355 prom\354nn\375ch, je\236 m\341 Maple zkoumat, lze jejich po\370ad\355 zadat jako druh \375 " }}{PARA 0 "" 0 "" {TEXT -1 55 " parametr; jinak si Maple \+ ur\350\355 sv\351 vlastn\355 po\370ad\355" }}{PARA 0 "" 0 "" {TEXT -1 85 " - pokud Maple ji\236 \236\341dnou prom\354nnou s kladnou relat ivn\355 cenou nena\232el, hl\341s\355 FAIL " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "pivotvar(-3+x1-x2+3*x3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#x3G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "piv otvar(-3+x1-x2+3*x3,[x1,x2,x3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%# x1G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "pivotvar(-3-x1-x2-3* x3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%FAILG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 448 28 "Ratio (soustava lin. rovnic " }{TEXT 449 1 "C" }{TEXT 450 11 ", prom \354nn\341 " }{TEXT 452 1 "x" }{TEXT 451 2 ") " }}{PARA 0 "" 0 "" {TEXT -1 106 " - funkce, kter\341 vyhodnot\355 pod\355ly, je\236 n \341m pom\341haj\355 rozhodnout, kterou novou prom\354nnou (resp. kte rou " }}{PARA 0 "" 0 "" {TEXT -1 94 " rovnici ze syst\351mu C) b udeme p\370id\341vat do nov\351 baze v r\341mci b\354hu simplexov\351 ho algoritmu" }}{PARA 0 "" 0 "" {TEXT -1 53 " - pod\355ly pro a_ik <= 0 jsou br\341ny jako nekone\350n\351" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 453 7 "Pozor! " }{TEXT -1 43 "Syst\351m C mus\355 b \375t v podob\354 z\355skan\351 p\370\355kazem" }{TEXT 455 7 " setup. " }}{PARA 0 "" 0 "" {TEXT -1 22 " - druh\375 parametr " }{TEXT 456 1 "x" }{TEXT -1 62 " zna\350\355 prom\354nnou, pro kterou se maj \355 po\350\355tat p\370\355slu\232n\351 pod\355ly " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "ratio([_SL1=10-5/2*x1-2*x3+x4,_SL2=3-1/2* x1+x2-1/4*x4,_SL3=1+5/2*x1-x3],x1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #7%\"\"%\"\"'%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 " \+ - z tohoto v\375sledku je patrn\351, \236e pivota bychom vyb\355rali z prvn\355 rovnice" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 4 " " }{TEXT 446 51 " Setup (soustava lin. (ne-)ro vnic, typ prom\354nn\351 - " }{TEXT -1 18 "voliteln\375 parametr" } {TEXT 447 1 ")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 " - tato fu nkce uprav\355 soustavu do podoby, kdy na lev\351 stran\354 rovnic jso u izolovan\351 prom\354nn\351 tvo\370\355c\355 bazi" }}{PARA 0 "" 0 " " {TEXT -1 92 " odpov\355daj\355c\355ho lin. prostoru, kter\351 \+ se nevyskytuj\355 na \236\341dn\351 prav\351 stran\354 lib. rovnice" } }{PARA 0 "" 0 "" {TEXT -1 101 " - dopl\362kov\351 prom\354nn\351 p ou\236it\351 k p\370evodu nerovnic na rovnice jsou ozna\350ov\341ny ja ko _SLi, i=1,2,..." }}{PARA 0 "" 0 "" {TEXT -1 85 " - prom\354nn \351, kter\351 jsou neomezen\351, jsou transformov\341ny na rozd\355l \+ dvou nez\341porn\375ch" }}{PARA 0 "" 0 "" {TEXT -1 103 " - v p\370 \355pad\354, \236e jako druh\375 parametr zad\341me jako typ prom\354n n\375ch NONNEGATIVE, jsou v\232echny prom\354nn\351 " }}{PARA 0 "" 0 " " {TEXT -1 32 " br\341ny jako nez\341porn\351 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "setup(\{2*x1+3*x2<=2, 3*x1+2*x2=4\} );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%#x2G,&*(\"\"$\"\"\"\"\"#!\" \"%#x1GF)F+F*F)/%%_SL1G,&\"\"%F+*(\"\"&F)F*F+F,F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 " " }}{PARA 0 "" 0 "" {TEXT -1 106 " V n \341sleduj\355c\355 kapitole 2 se bl\355\236e pod\355v\341me na komple xn\355 \370e\232en\355 \372loh simplexov\375m algoritmem, kde budeme" }}{PARA 0 "" 0 "" {TEXT -1 41 " pou\236\355vat kombinace t\354chto p\370\355kaz\371. " }}}}}}{MARK "0 0 0" 32 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }