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
theory and lecture notes of mos transistor inverter all along with the key concepts of inverter dynamic characteristics and power dissipation analysis of cmos inverter. tutorsglobe offers homework help, assignment help and tutor’s assistance on theory of mos transistor inverter.
Theory and lecture notes of Steps to Hypothesis Testing all along with the key concepts of Steps to hypothesis testing, homework help, assignment help and hypothesis testing tutors. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Steps to Hypothesis Testing.
tutorsglobe.com types of ionic crystals assignment help-homework help by online types of crystals tutors
identification of the fault in a given tv receiver - the tv receiver is switched on firstly. there is no picture just only retrace lines on the screen.
Nomenclature-Coordination number of complexes tutorial all along with the key concepts of IUPAC system of naming metal complexes, geometric isomers, Coordination number of metal complexes
basic thermodynamic concepts tutorial all along with the key concepts of First Law of Thermodynamics, Isothermal Process, Equation of Reversible Adiabatic Change, Temperature Change in Adiabatic Process, Enthalpy and Internal Energy, Specific Heats for Ideal Gases
tutorsglobe.com importance of senescence assignment help-homework help by online senescence tutors
tutorsglobe.com nitrogen fixation in legumes assignment help-homework help by online non-biological fixation tutors
tutorsglobe.com classification of markets assignment help-homework help by online definition of market tutors
gas law-ii tutorial all along with the key concepts of dalton's law, dalton's law of partial pressures, graham's law of diffusion, avogadro's law and its applications and gay lussac's law of combining volumes
the material control is guaranteed through laying down proper methods for storing, purchasing, issuing and minimizing material losses through identifying slow moving, obsolete, dormant material and also through minimizing scrap, wastages, spoilages and defectives.
Theory and lecture notes of Two phase commit protocol problem all along with the key concepts of two phase commit protocol problem. Tutorsglobe offers homework help, assignment help and tutor’s assistance on two phase commit protocol problem.
Cost Based Pricing - Actual Cost of Production, Full Cost Plus, Standard Cost, Marginal Cost Pricing.
there are two kinds of dc armature windings that are the lap and wave windings. for development of dc armature windings, a number of pitches related to the types of dc armature windings are back pitch, front pitch and winding pitch.
Industrial Chemical Processes I tutorial all along with the key concepts of Definition of chemical industry, Basic chemicals, Speciality chemicals, Consumer chemicals, Where are chemical sites located, Chemical industry: how environmentally safe, challenges for the chemical industry
1934896
Questions Asked
3689
Tutors
1474242
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!