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finsol - [RD E Find a fi[email protected] aigimimrs 8 $19 fameéioz...

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Unformatted text preview: [RD E. Find a}; figs: @633 aigimimrs 8:? $19 fameéioz: ”:2 \ '3 fifiiafiiz} 3 i1 ~§~ $272 —» $1262 amt? éemeggtraéze $3383: iii—e}; saiégfy the suificiené csnéétiazs pregenieé $37: $318 eiass. 5/3?” gwafiv‘a fg’gf/ “é 2. fising E‘Eewtan’s meifiad $0 finé fize Staiigfiary 301mg,- 9f 27“ as» g m _ rm 5 a mum «H 3%.; m M. 5% x52; 8 Q m w a; “a ru T. {w} 43.. we staid: ma}; E \ 1.2%.; 3. Pram mmggéememary séafimegg in knew pmgrammégg: 26% a3, be an {3;}351332 501mm}: $0 the 131392; pragmmmmg yyefiiem: Minimize 2: : Ea: Subgeci is Ax m 5}”, :1“: 2: {5 am}. Eat g5: he as; omimal sciatic}: ii} the é‘aaé gramem: Maximize as; m 553; gamed m A}? g c, €383} 2:3{3 m A???) x Q, s“ a ’1 3% , z 5% < *g “a (a; ‘g Mg :1» g M» ‘ 3 if“ i bii‘gmkfayézf,€¥m Effigx‘ngéfé LX?’ <1} 2i“; if” m a v5; ”/92 :3?” E f“ g g i; was? g; a {:9 Jfiég {1,51 41. Given the prefaéem Minimize fi$1,552?$3) 2 $1 suéjec’i t2} {221+3.)2+x§ 2 1 22:3: “in :52“ g 2 (a) Wriie the Lagmngiefi fizngtion flxbx‘g, A}? A?) of this problem as a fiifistmn of four variafiéeg. M r” E L. ; fwgfi/fi; =2 2 , é a , E. :33? 5329 ihfé; (b) Show mat {ML #1, 3/2, 1/2} is a. statieuary Emmi 0f 15(3519562; A1, 922). f: :5 $2225 ifi'fi} {c} Show that (—1, mi) is a "seguiiar point. if“ A. “2 “E 2,._ Q. 234 2 2.22% Ex 2;; 22; m :: K; 2 Mama; 2» 22:; 22,; E; E f :3: LE W}%<gw}§ ”fig? {3 if w'élfigtEgz/EK M Egg ,5, 4 = g; 2:2: EX Egi?’ Q 5 5 2:22 Zygfx g&§}§él&} 122% QE 5:2"; . E 2:92:22} Mg ~22} A 2 2% ”“i3“}<g WEE}? it 3 , ‘ z r“: / E§2Q§E-W€E~2;[é}5“¥?; EQT EM - ~22! E "a g ' :2 : 25%}5222225'3952222 g M, f E E E ~ Q I 2}“ E J E {:2} 2 :W{ («$2223} 2(2E Mg} / _ : 2’": Eli/”gig?” W5?“ “(2-2; 2:} M aim; 2:53; {$ng wig” fiéx; “If: W, N W 1.. g f i 3%% $E2; H. WE”? , E {.3 aéé f‘ g“ : 2:: 3.2:”; «w; : 5 E :2: MEWE if “X; g; fwfi“ Egg: 3 29% 5, find 253 ihe 100a} minimizers fer the: 13393916111 and demenstmte that they satisfy the safficient canditiem presentead in the dass. :vmme fix-:3 $2? $3) = x? + 1% + 2% subject, to :13; w :32 + :53 $1+$2+$3 Ii IE fl 4 W: $8rfflfigfi E % my 2: g§ f;%§&%fsw 5‘s; - “““““ M 1 MW' gfina if“; §§”§2%sfv}”e “iii-35$; 335%}: M ‘5 MW». fl M“EX=? fiflfifigzw ng Kg; &fl;% 5;”? g as: A i Q; ”.03 %§X§:i ?§X§:A Mg 5 gfigag 'W’Zigflg X it”; :: 35%;;35g if? "i“ 9‘3“; 5g} {(33%) m 5‘ g’ “#2: 39V§§W 29%;? f§;€.§,:§% I \WT/éF 1,52, E1 f 4}? is a 30683. minimize}: fez“ the problem \ EV’EHiZfiiZS f<$1_,$2,$3> : 333 — $2 subject- t0 E. Show tha‘é €va 2;; m 4% «1% r, W” H , Mm Q Q M; E _ s 3,; E? X; M 3 M A a4 q___§§ 2 4%; WV 13¢ a}? W. :53; a \VAME {1 wt, 2 W Q w {iii a; x23} A:_g§,,.§§§.§§.j $3.! a U . s is: «t 1 gem Mi ,,,,,,,, .V ,3 £3 5,15% M fiv 9 av g5 1 2 ‘ (fa! :1 «.13 wigs}... E; wigsséaaiaiig X? E, g; .5 g 5 W. 2 g 3 1:. 45 m w M 3m _____ as i M53352??? mu 3: x f “as; x. M Q 5 9 ET 3“ _ £5 {51% 3% Q t 1 w 3 m m x, 5;, x _______ a. E Kfi, WA; TESL by demonstrating that {MK/é? HZ, 11/54)? satisfies the sufficient csnéitions yes-exited .15 W E1 .33 ii;% M m w A“ i: i Q , g E w r a: 2 E . .53 7 ,V ,. A; m iJWr/f 335...? flaw“; a :1; .u an”): w m 5, X; g a, 3 fa , ”E. For $319 grobiem: Miflimize fig?) subfieci <0 352:2: 2 :5, let x“- be a. vesier such ithat 3% 2 5, Eet Z ‘96 a basis nuii space matr'm for A and 19% 6(2)} 2 fly? + Zv) be Zhe {aimed fanciign. Pram $33an if $3 m 5‘ «i- Zm is a vests}: with ‘3?th gaperty that them is a vector A3 sag-E1 that Vfia} 2 ATE.“ file}: $733133} x {3. 3 ff? flag ff 3’ 3* — f 3/; 3‘ ‘23 “E” 9353333 33 M 3:33 <3 {\fli 333 3:3; .2 3 3%,, am ng E w ' 4'“? a? 31% {/gxfié <3 %& ’ 3? 8. Find 3311 the ham} minimizers for the pi'afiiem Minimize f{$1, .1352) 3 33:? + x; - 331$; SIE1I3j81’3t to in which constraéat {2) is active an sansiraints {E} 8526i {3} an inactive} 8116i {£83193— strata thafi ihey satisfy the sufficient mmfitions presented; in the {:eurse. i C“ EWWWMWW fit“; ea :2 M; A"? ””5“ —§ IIIIIIIII mfigag’” M: if? E: : {IE : \f "35%)“; «EMME 22? E M? $33 5%.; 5i}; ES 9. Solve fie fofiowing linear pmgmmmigg prebiem by thQ simpiex 11197511062, staging with tfie ‘sasis {$3, :34}. Minimize z x ~2$1 W 33-2 subjectto xi¢x2425 2 2 32‘1"?"1132 T$4 “-3 3 $1$9,$3,$g 2 O 3 9; ~ « "a Ax fig ififi‘xfi gaff-3 §§"EQWX§W/{Q 52”??ng X; 59%er . A "2* Q Rf; ngé Zia; y§”§:xg=w'k& 5W3X§€2V k; W i; *' __3 M § m #9,”, ¥@5w%m Mam mf Kiwi? figmi”§R/QZ§§ {:35 MW; 2% ' 3J3?” ngé glfiswu 7% a . . 53%,? W M 72m 3 MM f i Q‘- 5 5 m f $(‘X i’égmiwfigwéfif Kg.“ ’3: (>- 3 § g s , m- g g ‘3 3 M.;m.gm‘“}§:‘w‘w ' w vjmfkéwqixfi WM .WM M "E‘I‘e nggmrgégx 333%”:[Qf 3%}; $3 {2* § 3 w img’ij? #5“ 3%i iX-‘gmzi; 3?“: 9:23“ 3”? mmg ”La i-“V *“ ”wafigfiwfigw f“ .. :6}ngng 5“ ’3‘ £2 £2; g3 a“? "‘ fgxg 1‘ng J; K“! 23 1E}. C(msider {like problem . , - : - 2 Mimrmze flwb 323,333) 2 :33? w?” $133233 — :54 Subjeci is m :m .m I My 8 h AYE d A. .H t1 m n M m A m T m... m A 1 % Mam 3T MM. umh , 2 I m x .M. .m M 3., g d 13 . .m n V 1 W a E a my MM. 8 any... wig} Emu/M 1.; n4 me... .% 0W, max 1% M d x .m MM 9...? @W $.5wa 5mm... mm. Q MW??? 9M .3 MM... A... M. -3......§......ia..} w... .M as E .3; MUM fiv 3.... 1...“! HM KM. M. ,,,,,,,,,,,,, g .3 gig?“ 44mg? .M M M. .13? 3515., g €2.23 Elisa ; as? Eshw . .5... M. M... MA”. .1. :23..a§§g2.wM 2...... . . .Mg M-§;;:: ; a; w; M W: .W. .2... .3 W M a... u M I; M figM:%§;%M My, vagas:;.;wMéj . a... M. , M. E M MM... (m: M ,,,,,,,,,,,,,,,,,, .1 .1311” fig»... .35.... Ly? 3?... «3H,. :xw Egg f: :2... %._M ME“. gm... My... M 13 aw» ,\ 2;... m. M...................,... Ma... 3%.-.. M... 3.. .5, MM. MM. .2. M... M... . g -E--............... .2... M MM is: ,,,,,, 33%} :izzaégxég _ . WW .3535. 4...; (2.2; it... MM. -3 M WK. Mv Mug .5: 7m M... Mia 5. 3“ MS a... Z A ,m mi; . . s. MEMM EM.“ My. AW}; MW}: g flux; 3:... 35‘ . 3%; 13%..» 3 1.3%. "9"“? «3...... M 1,. 3... Mi M MM. é... .MM. M Mg «2; déiié M.) 31%.; iiiiim i. my my $3. 5.... i mi; 33% g M? is .3. Essésazsiéw RAM 35:. gig}; M g “A w ..... sié...§a.: w .xiMmsM . 3” M a... “1% ewe. ‘35.. M, W mix)“ x2335. .5. .ng .5. 43....-.21 M M M 31. 3v 3...} . : M MM... w; m... M 5M. 4...... .1. 8 mm... 3.? 5%.... .... Min. M i. .1 “3;...“ w”? ‘1 M ééafiéfigiaisifizg.» f“? «5%....» . ..... $3.35.. .. i as}. \Ef; a gawk, fix. ..., ,,,,, z ...
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