Computational Procedure of Big - M Method, Charne's Penalty Method
Step 1 - State the problem in the standard form.
Step 2 - Then add non-negative artificial variable to the left side of every equations matching to the constraints of the type '≥' or '='.
While artificial variables are added, it produces violation of the corresponding constraints. This complexity is removed by bring in a condition which assures that artificial variables will be zero in the closing solution (provided the solution of the problem exists).
Alternatively, if the problem does not have any solution, then at least one of the artificial variables will appear in the end solution with positive value. This is attained by assigning a high price (per unit penalty) to these variables in the objective function. These large price will be designated through -M for maximization problems (+M for minimizing problem), where M > 0.
Step 3 - At last, use the artificial variables for the initial solution and continue with the usual simplex routine until the optimal solution is achieved.
Worked Examples
Example 1
Max Z = -2x1 - x2
Subject to
3x1 + x2 = 3
4x1 + 3x2 ≥ 6
x1 + 2x2 ≤ 4
& x1 ≥ 0, x2 ≥ 0
Answer
SLPP
Max Z = -2x1 - x2 + 0s1 + 0s2 - M a1 - M a2
3x1 + x2 + a1= 3
4x1 + 3x2 - s1 + a2 = 6
x1 + 2x2 + s2 = 4
x1 , x2 , s1, s2, a1, a2 ≥ 0
As it is known that, all Δj ≥ 0, optimal basic feasible solution is achieved
Thus the solution is Max Z = -12/5, x1 = 3/5, x2 = 6/5
www.tutorsglobe.com offers answering questions to types of barriers and curves of monopoly, economics assignment help- homework help.
tutorsglobe.com estimation of future cash flows assignment help-homework help by online capital budgeting and project planning tutors
tutorsglobe.com abscission and senescence assignment help-homework help by online reproduction biology tutors
tutorsglobe.com endocrine function of ovary assignment help-homework help by online functioning of female reproductive system tutors
www.tutorsglobe.com offers Area and Volume of Solid Figures homework help, assignment help, online tutoring assistance, geometry mathematics solutions by online qualified tutor's help.
tutorsglobe.com treatment of chlamydia assignment help-homework help by online chlamydia tutors
tutorsglobe.com environmental philosophy assignment help-homework help by online humanities tutors
www.tutorsglobe.com offers acids and bases homework help, acids and bases assignment help, online tutoring assistance, inorganic chemistry solutions by online qualified tutor's help.
Theory and lecture notes of Real Zeros of Polynomial Functions all along with the key concepts of Long Division of Polynomials, Remainder Theorem, Synthetic Division, Descartes' Rule of Signs, Rational Root Test, Upper and Lower Bounds. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Real Zeros of Polynomial Functions.
Production planning can also very much assist in cost reduction. The location and lay-out of the factory have important affect on cost.
Lagrange and Hamiltonian Mechanics tutorial all along with the key concepts of Frame of Reference and Constraints of Motion, Constraints of Motion, Generalized Coordinates and Degrees of Freedom
tutorsglobe.com c3 and c4 pathways assignment help-homework help by online plant physiology tutors
tutorsglobe.com herpes virus replication assignment help-homework help by online herpes viruses tutors
Zoogeography-Neartic and Neotropical Regions tutorial all along with the key concepts of Fauna of the Nearctic Region, Neotropical Region-bird continent, Composition in the Nearctic region
Superposition of Waves II tutorial all along with the key concepts of Coherent Sources, Interference of Waves from Two Slits, Intensity Distribution in Interference Pattern, Interference in Thin Films, Fraunhofer Diffraction by Single Slit
1950962
Questions Asked
3689
Tutors
1473558
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!