Applied Max-Min Problems - fiPPLIED...

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Unformatted text preview: fiPPLIED l7fi¥l0Ufl~fllNanfl PROBLEDS .' J'I/ my To ILLUSTIMIE 1‘06 GENEML PERM/PE: 0F 771555 P12051505 Mun $005 RULES OF wane F012 50L vwa WEI) LUITH l9 SInPLE EXANPLE. THEN wE'LL 60 77117006» A munBER 0F DOFE INVOLVED ElonPLES, I00 F7 00" FENCING IS HUfiILfiBIE 6017'” AJHICH To Emcms's » 05c mmcuw/z canoe». ONE SIDE OF we came» IS To BE ALONG me .9106 0F a wuss 9W THEREFME Raga/tees No FENCING. Maw $110010 ms DmEmSIoms OF ME G‘FM’DEN as cm)me ml wens)? ro next/7126 77:5 ENCLOSED 19/759 2 GEMEIML FEATURES : CHOOSE SODETHING ma, omsnmoms ) IN ORDER 7'0 nfixlmzs on mm:sz sonemma ELS'E (13.6.J mm). Pxocsoues : Maw 0 PICTURE (IF Poss/ms ) nmo INTRODUCE [VB/IE: Fol? THE mm: yaw BEE To choose am) we WINé To BE mama/250 OR nwmIZED. ‘- - LENG w 0F amps” )1 = Mon; 0F armom fl = new 0F 6080510 meE 7»: mm To BE naxlmasp/mmmeso w TERI): OF 7715 THINGS To 86 cuossm : /9=xy USE fiN)’ Comsmmmr IflPoSED on 1725 way you can naxe’ yaw? CHOICE c 5.6., army Ianr OF FENCING flVfilLfiBlE ) To 51.117”va 9L1. BUT awe 0F DIE " 61mm: ” WWW/981.55. 100 x 05 ‘< u]. ‘<. I! y = 5'0-jx fl=xlfo~ x) .L 8. 2. mm = 50x- ix TIiE RESULT I5 0 FUNCTMN OF ONE VHRIABLE . IF 1715 198081.50 II'IP06‘ES l9 Rssmlcnom om VfiLUES 0F DIE cue/c5 vfimfime , meE IT as am INTERVAL,‘ asxsroo None: .77 flfi)’ SEE/7 5/11.)“ To INCLUDE X30 0N0 X=IOO SINCE 8077/ 6105 fin) 0350 OF 0, Bar 9 CLOSED zmTEIBML :5 fiLwfiYS PREFERfiaLE .9ch masoer nfixmfi an») film/r10 mwnys EXIST. mow FIND 7775 nfixmun/mmmun Val-us OF THIS FUNCTION on) rms wrskvaL, nfixzmze flax) = 502p :- xz an) £0,100). cmncm. POINTS : fl'cx) = SD-X ‘X: 5'0 19:50) : 50(50) — 51- Mo)" ENDPoIrvTS : naxmun 0F mm F7": was/v x:.fo Fr y = 50'1-(50) =45” DORE EXBUPLES : 2. n fiscrnmcvmk ENCLosuPE IS TD :35 Cowsmucnso wmw mm we r7" nmss swss me To as maps 0; Wu» c cosr : I 79-” pm FT ) m 1715 FOURTH SIDE IS TO BE "908 OF CEDS‘NT BLOCK (cos'r : liq” Pei? PT ), wlmr omemsmws MILL. rmwsz we can ,2 W ODD 3m»! 7 600 F7 1 y wow WOOD C = c057 C = 7x +77: 1! '7)! +14} a ulx+.2))l comsmmm‘ : xy 2 60° - 600 7 x was, c = 147: + .‘u ( 9;? ch) = mx + nesmtcnom : x > a 1.2.4» mtwsz ch) = 14x 4 x on) (0,00 > I a» N075 mm lm £qu + 5-26—63) = ‘0 .9va lm U4“ 3,7“ )=°° x-vvo x-va" so 777505 15 an: 198501.076 mmmun an: my») mm 0051' occuR 97 I? CRITICAL POINT, I:,wo I cax): l‘i' '75? DEFINED EVERYwfiERE on) (emu) . c’cx) .-. o wntm 2' I236” X = =900 x: 30 (sch x>o) nmmun COST .’ :2 we C(30) = Mason ——-----—;0 = ’ew OPTION. DIDENSMIOS 1 x = 30 FT y : 23—052 : .20 FT 1) SQUARE SHEET OF 090030320 .20 no a» 0 SIDE IS To BE USED 10 nan: mu cram TOP Box BY currwc a 3mm. mama Fkofl 5ch coRMEI? mvo THEN Fowwc THE SIDE! UP. you) 2.31265 :9 $0039: SHOULD 86 our Fkon EACH CMPNER To mam/7125 7);; Val. was of THE Resumma eox :’ X = $105 Lemar» of THE seam: cur ouT .10 \l = vowns or 1116 RESULDMG 86K imiii] FOLD FLM’: UP HLOM€ 1 ("W ova-.22 5 : 5 3 ms Dona» woes _ fl , a 20-4): v = l. 1.5106?» )( mom )wsmur) = (no wanna—ax) (x ) 3 2. Van) = 1H -80): HMO): osxslo 4 (3x73 90x +100) V’tx) = tax"-wa+t/oo = 1/ (3x-I0th-Io) Cleman Powrsuu (043(410): x: 3—;- v = (.20- 959)(ao-§£)c31‘) ID (-5-) Le _ 19,090 V‘s)‘ 9 END POINTS .' "'0", H03 wHEW X = 2' W q 3 nfixmun voLvnE 0F 3. c Sfiwmu. PROBLED' ) FIND THE fiEcmNGLE 0F naxmm. 192519 17197 can) as ImscRIBED w a CIRCLE 0F RmeS 1 , 'X 1' LENGTH OF PECTHNG'Lf y y : wmn] 0F eacmmae I9 = 0959 0F kscnmaus PYTHflGonEnm 771601350 GIVES II A: xliy‘L CRITlCfiL POINTS m (0,4) : J- .L 1- ‘2 Na) : (1(H-u‘J‘)’: xtfi-m-x‘) (—2.9) + upx’)’ .L J. - xlwd‘) ‘ + H-x') ’- H qu‘fi (-3“ 4- UMP) ) H-ax‘ VH-x‘ II ‘4. 4-121 Mx) = my, IS DEFINED svskywvme on (0,.2 ) ma EQUBLS‘ 0 omy «20510 1-1-3):2 :0 x"= ~7- Xzfi— L-Easmw (0,2)) fluff) = 1/3: {ll-(EV = flff ME) = .1 smnpmms : nnxmun MEI) 0F .2 wIIEN 1:6— y : ‘y/‘l-tfi)‘ = .5 FIND THE POINT ON THE GIMP/i 0F y: X‘ T891 IS CLosEsr Ta ms PolNT ( 18, 0). z 7 7" rmwmzs we Lemar» L 0F THE LINE Jomms £18,») war” a Panw on THE GIMP» FDRflULH’ FOR Lx‘y) = (x, x1) 0", m L = V cat-:9)“- Ly-o)‘ -.-. ‘/ cx-29J"+ mtg)" = VX"4x"-3cx+3.w M -‘ 17 tom. smnmy THE nmmnsnc To name mar mmmzwc Tins IS' 1716 $005 05 nwamzwc ch) : xq'l' X1-36X 4 3-2"! SINCE lm Put) = Im Put) a °° 771ka 15 an 19850wa Dire/nun X4” x->-°° wmcu 0057 ocean 07 0 cmmm. POINT, Pltx) : 4x3+ax '36 ONE Sownon 15 Easy TD FIND B)’ :NS'PEcnom : x: .2 was, 1x3 +x ~18 has a mom? 0F x-a, To FIND 1772 mg FfiCTDR JOE DO 3 DIVISION .‘ 2):" + #3: +7 Y-aje’Lx’ +ox" +x-18 2x3 ~‘IX1' Hx‘+x Alf-9x M ‘Ix-Is fix ~13 77105, a ax3+x-Ie = cx-auax‘wxm) $0 1x3“: ~18 -‘- 0 cx-axuzwvm) = a l . x—a:p 4X. mas ONLY (:00wa RooTs SINCE bz-‘Iac = III-Han?) ‘ 0 X's-1 comssausmnr, THERE I; ONLY one «man Ponw, «mm» 0057' GIVE THE BBSOLUTE mmnun, c 1.05551 PomT cx,x") = (-2, ‘1) IO. ...
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Applied Max-Min Problems - fiPPLIED...

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