Graphical solution to a 2 variable lp to find the

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Graphical Solution to a 2-Variable LP
X1
X2
10 20 40 50 60 80
finishing constraint
carpentry constraint
demand constraint
z = 60
z = 100
z = 180
Feasible Region
G
A
B
C
D
E
F
H
To find the optimal
solution, graph a
line on which the
points have the
same z-value. In a
max problem, such
a line is called an
isoprofit line while
in a min problem,
this is called the
isocost line. The
figure shows the
isoprofit lines for z
= 60, z = 100, and
z = 180

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Graphical Solution to a 2-Variable LP
The last isoprofit
intersecting
(touching) the
feasible region
indicates the
optimal solution for
the LP.
X1
X2
10 20
40 50 60 80
finishing constraint
carpentry constraint
demand constraint
z = 60
z = 100
z = 180
Feasible Region
G
A
B
C
D
E
F
H

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Graphical Solution to a 2-Variable LP
The optimal
solution must lie
somewhere on the
boundary of the
feasible region.
The LP must have an
extreme point that is
optimal, because for
any line segment on
the boundary of the
feasible area, the
largest z value on that
line segment must be
assumed to be at one
endpoint of the line
segment.
X1
X2
10 20 40 50 60 80
finishing constraint
carpentry constraint
demand constraint
z = 60
z = 100
z = 180
Feasible Region
G
A
B
C
D
E
F
H

Summary of the Graphical Solution Procedure for
Maximization Problems

Prepare a graph of the feasible solutions for each of
the constraints.

Determine the feasible region that satisfies all the
constraints simultaneously.

Draw an objective function line.

Move parallel objective function lines toward larger
objective function values without entirely leaving the
feasible region.

Any feasible solution on the objective function line
with the largest value is an optimal solution.
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