Problem 1: (Use the below graph sheet for solving )

Use the graphical method to solve the given LPP:

Maximize Z = 2x₁ + x₂

ST

x₂ 10

2x₁ + 5x₂ 60

x₁ + x₂ 18

3x₁ + x₂ 44

and x₁ 0, x₂ 0

Solution:

Constraint 1:

X1
X2

Coordinates ( , ) and ( , )

Constraint 2:

X1
X2

Coordinates ( , ) and ( , )

Constraint 3:

X1
X2

Coordinates ( , ) and ( , )

Constraint 4:

X1
X2

Coordinates ( , ) and ( , )

Coordinate	Objective function value

Optimal Solution:

Z =

X₁ =

X₂ =