Question

please help i cant seem to get the steps right

68. Minimize P 20x + 30y subject to the following constraints. 3x+y 9 y x y 2 x0

Answer 1

P 20x+30 To minimize Subject to the constraints 3x+y9 2 is above the line the Constraint The regin presentiy 2 Lihed =is included) The yegim epresentiy to the Yaxis Hh Constraint o s iyut ( 1-axis is included to the cemstraint 3u+ysg Equation correspnding 3x R1X-x wo → 3メ+0-3 > 3u-9→Xミ3 an yaxisS 3-l0)+ 9 >79 raph 3+jg is tha strainut line joiig he pojnts (3 0) and CO9).Let hu Lihe be L Line Ldindes plane into tuo half planes. Putti the ongin in th constrait the Coordihates 3 0+059 oく9, which is correct. The half-plana containi he oiih presets the comtrait 3 we shode it. CBlack) EqMatiom coeendiy tb the constraint n is Tts groph is a Straight Paseh thrmp the orith, and it Slope is 1. We drau his Liue. Let this Line be L he Constraint s abouve the ina L we shade it. (Red)

7L2 e99) A 2,2) X Intersecting Point te Lines Land L from & and Poit a intersecti an aud Lis 8 21). 2nkersectring Paint oLine zn and 2 is AC2,2) .. The feasi'S Le rgisn is as shaded in ta greph. Its Corner pnht A(2,2), (22), S (0.3),D C0,2 objectiv funchian is are * The p 20x430 At A(2,2), Pe20(2) 30(2) 49t60 100 B22 P-2012)+3o)= At 180-+276 l12.50 At C(o9) P 20C0)+3J0 (S) 0+ 270 2270 At D(o,2) P 20(0) 30 (2)0t6 o 60 inanm p6O at n0, 2