Graphical Solution Procedure sample assignment and solved questions, free examples and solved homework samples for Graphical Solution Procedure in operation research.
Question: Max Z = 80x_{1} + 55x_{2}
Subject to
4x_{1}+ 2x_{2 }≤ 40
2x_{1} + 4x_{2} ≤ 32
x_{1 }≥ 0 , x_{2 }≥ 0
Answer
The first constraint 4x_{1}+ 2 x_{2 }≤ 40, can be written in a form of equation
4x_{1}+ 2 x_{2 }= 40
Place x_{1} =0, then x_{2} = 20
Place x_{2} =0, then x_{1} = 10
Therefore, the coordinates are (0, 20) and (10, 0)
The second constraint 2x_{1} + 4x_{2} ≤ 32, can be written in a form of equation
2x_{1} + 4x_{2} =32
Place x_{1} =0, then x_{2} = 8
Place x_{2} =0, then x_{1} = 16
Therefore, the coordinates are (0, 8) and (16, 0)
The graphical presentation is
The corner positions of feasible region are A, B and C. Thus the coordinates for the corner points are
A (0, 8)
B (8, 4) (Crack the two equations 4x_{1}+ 2 x_{2 }= 40 and 2x_{1} + 4x_{2} =32 to obtain the coordinates)
C (10, 0)
We are given that Max Z = 80x_{1} + 55x_{2}
At A (0, 8)
Z = 80(0) + 55(8) = 440
_{ }
At B (8, 4)
Z = 80(8) + 55(4) = 860
At C (10, 0)
Z = 80(10) + 55(0) = 800
The maximum value is achieved at the point B. Thus Max Z = 860 and x_{1} = 8, x_{2} = 4