Question

Min Z = 6X1 + 4x2 Subject to Xi + 2x2 > 2 -X1 + 2x2 5 4 3x1 + 2x2 < 12 X1, X2 > 0

Answer 1

Ano Min z = 6 xxt 442 Subotom 8172307 32 - 3 24+242 3. 4 321+272512 - 0 . X1, X₂ 7,0 Solved coing Graphically 0 21+2.42 = 2 - X4+ 272 = 4 it x1=0, x2 = 1 (0,1 lit X130, X2= 2 (0,2) it X2=0., 22=2 (200) 1 + x2-0, 31=-4 74,0) Point = (x7,x2) =(2,1) I point = 1 {1, Kı) = 64,2) ☺ 38, +2X2 =12 if 220 , x2=6 C0,6) it Iz = 0, 41=4 (4.0) Point =(2, X2) =(4,6) g/+22252 -xit222=4 4x2= 6 =) X2=3/2=105 xit 2x1.5 = 2 X = 2-3= -1 71221 Feasible Region 76,25 -1312) T o ,1) -54-4 -3 -2 -1 2 & 4 5 0 1 21-4

Values of Function At (012) Z = 6 27+ 4X2 =16 XOlt (4x2) = 8 1238 At could 2 =621+4 X2 =66x0) 44x1) = 4 2-4 At 1-1,3/2) Za 6x17 4X2 = (6x+1)+(4x3) = -6 + 6 =0 2=0 Min Z=0 at 1-3 312) Hence, the optimal solution is x = 4, X2=3%