Math Project

HOAEOL K S SolUTIONS O

Fvs problem Miini: X, ax,X4 subd to X +3x, |

X2x,Xy 3x, X X, X4

at (0,0 , i). Tu ttbool solvkion giv This is INCoRNECT becav Violals 4u CunstiaiAt:

AS

Cis nh a FS)

T cofrt solutionis z 4 ot (,, 0,0). L Asssfmt:

Q)@ Oriqinal: Maxiiw 20x, +30x Suje to Sx,- 4 X loo

X,Ix, s 40 X Soo

Mnmie: l00 y, + 90 S 00

sujut t Sy, Ya Dual

4y,12y 30 Y,Y,Y2o

bOr gnal: Mini mite: x, - 3x

-30 Svbjct 4o 6x, xa2 30

X, , X o Cbufort dval, ud ta flip 4 setond fhird iAlitis!)

Maxii: -30y,*SOy-303 Svbj c

Dval Y Y2 y,tyY $ *S -3

Y.,Y,Y0

Ori ainc: M4xiniit: -X, dx stt y: 5x, + X S 60

3x, x2 10 lip X,20

Misini: 60y, -

10 y* d0 y bjtt Fo* Sy.3y +_y» 1

Y }y

sbj to

Dual Mimit y,* Ya sbjt to : Y .

-2

Y,,YO0

Suithh dvd to nax flie 4 2 ongtsaint MAXimie: Y,y Svbjct bo y,

Y

Mudels a extt ly Sa

Oriqine: maximitt: X-x 3x, sbjatto X, + ax>| flip

3 X, XO0 X UnrtSHic tad

Adjsted Mimitc X,*2X* S X3.

X,-3x* 2X,*SX

*SX3 3

3

Mjaiit:y,2Y 3y,-3Y4 Y y yu

-3y3 *Y subut tu

y3yYa 2 -3

Al ystd MAXi: Y,y2-S(y, Y4) sbj tu

*3 Y4) -3y 3

Let Y-Y Ys Tu

Maximite: Y, *dy 3 Ys sbttt to

3 2-3 Y.,YaY Thisis 44 san S ori origintl node

T dv probkn isi MaxiL 36y.*0y,oP1 Sbe to 374y 2y, 1L0

67. 67' ?y 400 6y,Sy '4y, S 300

.,Ya,Y26

qet ind municu fof m: Miniaita: 367,-20 y30 y,

SY,y 2y, +y, 60 67.69y, *Ys :400 6y,*3y4 y 300

sbut

Plun iLAssiskto Gat Mx : )950 at (,0, 2)

T psudu4ion cost of scitl q6sthr (y 21 T VPwld be vaheyi itL 4Ks asvt, S. tngto onvna 4n qovtrn at to înurui prissu t prudditn cus} uovl not s

Mode| is Mii 600y,-1oo0 y, 300y, 3So y, +4o0 ,4S0 0 y

$30 t,t 4S

SSo Ya

Y. Ys, i4, Ys, Y. vnrskiedd 1f O o uArstsidad yuisbus (S, Y is ngskiu utt had side of h fivst con strant, Yy,, ALLAYS bi ngshu (snu y,0).

prss Jffacna hatyan hou mveh 4 4 Fagten Narhurtu d

hos sls btk for. Th3 vtlt uvld iad ud ne fos a poos bvsss Md ' hw thtif

4ship

erAS Si amn f ahjthi fvntkin CPops thou o y h autvll solnd

4Lis in LP Assist nt oiut effurt) So ths. Fur on, Thr at n nvnbur ot

shiaw vld sinply nst purch tho 100 AHrih CAAS

beak o 4h syylnft kaport atin, o ster hn f a fixid cost