Problem 3:

Use the graphical method to solve the given LPP:

Minimize Z = 3x₁ + 2x₂

ST

x₁ + 2x₂ 12

2x₁ + 3x₂ 12

2x₁ + x₂ 8

and x₁ 0, x₂ 0

Solution:

Constraint 1:

X1
X2

Coordinates ( , ) and ( , )

Constraint 2:

X1
X2

Coordinates ( , ) and ( , )

Constraint 3:

X1
X2

Coordinates ( , ) and ( , )

Use the below graph sheet for solving:

Coordinate	Objective function value

Optimal Solution:

Z =

X₁ =

X₂ =