Question

Find the maximum value of Z= 4X₁ + 6X₂

where X₁ , X₂ ≥ 0 and

subject to the following constraints.

- X₁+ X₂ ≤ 11

X₁+ X₂ ≤ 27

2X₁+5 X₂ ≤ 90

Answer 1

Max z = 481 +682 To draw constrain we treat it as equlity -24 +22 11 -0 (straish ling) ie -x + 22 = 11 constraints as equlity traw a the a o 1-1 21 To be two points straight line be two points on To € drow constraints 21+22 The corresponding equation 21+22=27- (2a) responding equation Talo 127 T 27 o be two straight points on the line. To draw The corresponding er constraints 224,45 22 290 reponding equation 294 +5%2 = 90 x 72 0 457 be two boints Lo straight on the line. 18 Now we will draw a eagh rough sketch of the above three een and 24=0, y = 0 122 0 | Hence the region bounded I by ABC DE A= (0,1) 7=424+6X2 = 4*0+ 6*11 = 66 B=(5, 16), solving eso ((a) and ßa) Z- 116 1 c = (15,12) , solving ean (3a) and (19) - += 4*15+ 6*12 = 132 D = (27,0) solving (29) and 22=0 7 = 108 EF (0,0), =0 Hence May Z = 132 net nieIS, 2 =12

Soln: Max z =132, at x1=15, x2=12