Special or Unique Cases in Graphical Method
Multiple Optimal Solution
Example 1
Solve by means of graphical method
Max Z = 4x1 + 3x2
Subject to
4x1+ 3x2 ≤ 24
x1 ≤ 4.5
x2 ≤ 6
x1 ≥ 0 , x2 ≥ 0
Answer
The first constraint 4x1+ 3x2 ≤ 24, can be written in the form of equation
4x1+ 3x2 = 24
Place x1 =0, then x2 = 8
Place x2 =0, then x1 = 6
Then coordinates are (0, 8) and (6, 0)
The second constraint x1 ≤ 4.5, can be written in the form of equation
x1 = 4.5
The third constraint x2 ≤ 6, can be written in the form of equation
x2 = 6
The corner positions of feasible region are A, B, C and D. Therefore the coordinates for the corner positions are
A (0, 6)
B (1.5, 6) (Solve the two equations 4x1+ 3x2 = 24 and x2 = 6 to obtain the coordinates)
C (4.5, 2) (Solve the two equations 4x1+ 3x2 = 24 and x1 = 4.5 to obtain the coordinates)
D (4.5, 0)
We are given that Max Z = 4x1 + 3x2
At A (0, 6)
Z = 4(0) + 3(6) = 18
At B (1.5, 6)
Z = 4(1.5) + 3(6) = 24
At C (4.5, 2)
Z = 4(4.5) + 3(2) = 24
At D (4.5, 0)
Z = 4(4.5) + 3(0) = 18
Max Z = 24, which is accomplished at both B and C corner positions. It can be attained not only at B and C but at every point between B and C. Thus the given problem has multiple optimal solutions.
No Optimal Solution
Work out or solve graphically
Max Z = 3x1 + 2x2
x1+ x2 ≤ 1
x1+ x2 ≥ 3
The first constraint x1+ x2 ≤ 1, can be written in the form of equation
x1+ x2 = 1
Place x1 =0, then x2 = 1
Place x2 =0, then x1 = 1
Thus the coordinates are (0, 1) and (1, 0)
The first constraint x1+ x2 ≥ 3, can be written in the form of equation
x1+ x2 = 3
Place x1 =0, then x2 = 3
Place x2 =0, then x1 = 3
Thus the coordinates are (0, 3) and (3, 0)
There is no common feasible region produced by two constraints combine, that is, we cannot find out even a single point which satisfies the constraints. Therefore there is no optimal solution.
Unbounded Solution
Example
Solve through graphical method
Max Z = 3x1 + 5x2
2x1+ x2 ≥ 7
x1+ x2 ≥ 6
x1+ 3x2 ≥ 9
The first constraint 2x1+ x2 ≥ 7, can be written in the form of equation
2x1+ x2 = 7
Place x1 =0, then x2 = 7
Place x2 =0, then x1 = 3.5
Hence, the coordinates are (0, 7) and (3.5, 0)
The second constraint x1+ x2 ≥ 6, can be written in the form of equation
x1+ x2 = 6
Place x1 =0, then x2 = 6
Therefore, the coordinates are (0, 6) and (6, 0)
The third constraint x1+ 3x2 ≥ 9, can be written in the form of equation
x1+ 3x2 = 9
Place x2 =0, then x1 = 9
Hence, the coordinates are (0, 3) and (9, 0)
A (0, 7)
B (1, 5) (Solve the two equations 2x1+ x2 = 7 and x1+ x2 = 6 to obtain the coordinates)
C (4.5, 1.5) (Solve the two equations x1+ x2 = 6 and x1+ 3x2 = 9 to obtain the coordinates)
D (9, 0)
We are given that Max Z = 3x1 + 5x2
At A (0, 7)
Z = 3(0) + 5(7) = 35
At B (1, 5)
Z = 3(1) + 5(5) = 28
At C (4.5, 1.5)
Z = 3(4.5) + 5(1.5) = 21
At D (9, 0)
Z = 3(9) + 5(0) = 27
The values of objective function at corner points are finding as 35, 28, 21 and 27. But there exists infinite or countless number of points in the feasible region which is unbounded. The value of objective function will be higher than the value of these four corner positions, that is, the maximum value of the objective function takes place at a point at ∞. Therefore the given problem has unbounded solution.
Email based graphical method assignment help - homework help
We at TutorsGlobe offer special cases of graphical method assignment help - homework help, Multiple Optimal Solution, No Optimal Solution, and Unbounded Solution in operation research subject. Our specialized operation research tutors can help you in solving your complex graphical method based problems; we offer step by step unique answers for each and every problems and its help you in solving same kind of problems in future without any external help.
Why TutorsGlobe for graphical method assignment help
tutorsglobe.com mixed economy assignment help-homework help by online economic systems tutors
tutorsglobe.com criticism of marshall statement assignment help-homework help by online alfred marshall’s definition tutors
tutorsglobe.com industrial production of penicillin assignment help-homework help by online penicillin production tutors
Quantitative-Polygenic Inheritance tutorial all along with the key concepts of Continuous Variation, Other Considerations and quantitative inheritance
Theory and lecture notes of Rational Functions and Asymptotes all along with the key concepts of Vertical Asymptotes, Horizontal Asymptotes, Holes, Oblique Asymptotes. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Rational Functions and Asymptotes.
liquids tutorial all along with the key concepts of comparison of liquids with gases and solids, structure of liquid, properties of liquids, cohesion and adhesion and viscosity
www.tutorsglobe.com offers languages and maintainability homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
Transport and Diffusion Equation tutorial all along with the key concepts of Fick's Law, Equation of Continuity, Diffusion Equation, Boundary Conditions
Manufacture of Sulphuric acid and Sulphates tutorial all along with the key concepts of Manufacture of Sulphuric Acid, Contact Process, Manufacture of Sulphates
Theory and lecture notes of Satisfiability of Boolean expressions all along with the key concepts of satisfiability of boolean expressions, Complexity P & NP, SAT, Cook theorem, De Morgan’s law, Distributive law. Tutorsglobe offers homework help, assignment help and tutor’s assistance on SAT.
tutorsglobe.com analysing and interpreting financial statements part ii assignment help-homework help by online financial accounting tutors.
tutorsglobe.com dewars method assignment help-homework help by online isolation of noble gases tutors
tutorsglobe.com classification of gymnosperms assignment help-homework help by online spermatophytes tutors
tutorsglobe.com effects of global warming assignment help-homework help by online global warming tutors
Cash Flows from Operating Activities, is the net outflow or inflow from trading operations, after tax payments (or receipts) and cash paid to meet financing costs.
1960695
Questions Asked
3689
Tutors
1450965
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!