Maximize z= 3x₁ + x₂ Subject to the constraints x₁ + 2x₂ ≥ 2 2x₁ + x₂ ≥ 2 x₁ + x₂ ≤2 X1, X₂ ≥ 0

Question

Solve the following LPP by two phase method Maximize \( z=3 x_{1}+x_{2} \) 

Subject to the constraints \[ \begin{array}{l} x_{1}+2 x_{2} \geq 2 \\ 2 x_{1}+x_{2} \geq 2 \\ x_{1}+x_{2} \leq 2 \\ x_{1}, x_{2} \geq 0 \end{array} \]

Answer 1

 

For line x₁ + 2x₂ = 2,

x1	0	2	2/3	-2
x2	1	0	2/3	2

For line 2x₁ + x₂ = 2,

x1	0	1	2/3	2
x2	2	0	2/3	-2

For line x₁ + x₂ = 2

x1	2	0	1	-1
x2	0	2	1	3

\(\triangle\)ABE is feasible region whose corner points are A(2, 0), B(0, 2) and E(2/3, 2/3).

Corner points	Objective function max Z = 3x1 + x2
(2, 0)	6(max)
(0, 2)	2
(2/3, 2/3)	8/3

\(\therefore\) solution of given linear programming problem is x₁ = 2, x₂ = 0 and max z = 6.