General Linear Programming Problem (GLPP)
Maximize / Minimize Z = c1x1 + c2x2 + c3x3 +.................+ cnxn
Subject to constraints
a11x1 + a12x2 + .............+a1nxn (≤ or ≥) b1
a21x1 + a22x2 + ...........+a2nxn (≤ or ≥) b2
.
am1x1 + am2x2 + ..........+amnxn (≤ or ≥) bm
&
x1 ≥ 0, x2 ≥ 0,..., xn ≥ 0
Where constraints may be in the terms of any inequality (≤ or ≥) or even in terms of an equation (=) and at the end fulfill the non-negativity restrictions.
Steps to change GLPP to SLPP (Standard LPP)
Step 1 - First of all, write the objective function in the maximization form. If the known objective function is in minimization form then multiply all through by -1 and write Max z? = Min (-z)
Step 2 - Then, convert all the inequalities as equations.
o If an equality of '≤' appears then add a variable called Slack variable. We can change it to an equation. For instance x1 +2x2 ≤ 12, we can write as
x1 +2x2 + s1 = 12.
o If the constraint is of '≥' type, we deduct a variable known as Surplus variable and change it to an equation. For instance
2x1 +x2 ≥ 15
2x1 +x2 - s2 = 15
Step 3 - After that, the right side element of every constraint should be made non-negative
2x1 +x2 - s2 = -15
-2x1 - x2 + s2 = 15 (Multiplying throughout by -1)
Step 4 - All variables should have non-negative values.
For instance: x1 +x2 ≤ 3
x1 > 0, x2 is unrestricted in sign
Then x2 can be written as x2 = x2? - x2?? where x2?, x2?? ≥ 0
Thus the inequality takes the shape of equation as x1 + (x2? - x2??) + s1 = 3
Using all the above steps, we can change or write the GLPP in the form of SLPP.
Write the Standard LPP (SLPP) of the following
Example 1
Maximize Z = 3x1 + x2
Subject to
2 x1 + x2 ≤ 2
3 x1 + 4 x2 ≥ 12
& x1 ≥ 0, x2 ≥ 0
SLPP
2 x1 + x2 + s1 = 2
3 x1 + 4 x2 - s2 = 12
x1 ≥ 0, x2 ≥ 0, s1 ≥ 0, s2 ≥ 0
Example 2
Minimize Z = 4x1 + 2 x2
3x1 + x2 ≥ 2
x1 + x2 ≥ 21
x1 + 2x2 ≥ 30
Maximize Z? = - 4x1 - 2 x2
3x1 + x2 - s1 = 2
x1 + x2 - s2 = 21
x1 + 2x2 - s3 = 30
x1 ≥ 0, x2 ≥ 0, s1 ≥ 0, s2 ≥ 0, s3 ≥ 0
Example 3
Minimize Z = x1 + 2 x2 + 3x3
2x1 + 3x2 + 3x3 ≥ - 4
3x1 + 5x2 + 2x3 ≤ 7
& x1 ≥ 0, x2 ≥ 0, x3 is unrestricted in sign
Maximize Z? = - x1 - 2 x2 - 3(x3? - x3??)
-2x1 - 3x2 - 3(x3? - x3??) + s1= 4
3x1 + 5x2 + 2(x3? - x3??) + s2 = 7
x1 ≥ 0, x2 ≥ 0, x3? ≥ 0, x3?? ≥ 0, s1 ≥ 0, s2 ≥ 0
Some fundamental Definitions
Solution of LPP
Solution of LPP is any set of variable (x1, x2... xn) which satisfies or fulfills the given constraint.
Basic solution
It is a solution achieved through setting any 'n' variable equivalent to zero and solving remaining 'm' variables. These 'm' variables are known as Basic variables and 'n' variables are known as Non-basic variables.
Basic feasible solution
A basic solution that is feasible or possible (all basic variables are non negative) is called basic feasible solution. There are two kinds of basic feasible solution.
1. Degenerate basic feasible solution
If any of the basic variable of a basic feasible solution is zero (0) than it is referred to as degenerate basic feasible solution.
2. Non-degenerate basic feasible solution
It is a basic feasible solution which has precisely 'm' positive xi, where i=1, 2, ... m. In other terms all 'm' basic variables are positive and left over 'n' variables are zero.
Optimum basic feasible solution
A basic feasible solution is referred to be optimum when it optimizes (max / min) the objective function.
Email based Linear Programming Assignment Help - Homework Help
Do you stressed out with linear programming questions? Are you not finding exact answers for linear programming assignments? We at www.tutorsglobe.com offer Linear Programming assignment help, Linear Programming homework help, Linear Programming projects help and online tutoring assistance. Professional degree holder tutors are avail for 24x7 hours and offering best support materials for operation research and linear programming concepts and theory. The Linear Programming problems can't be solved without clearing concepts and without knowing each step followed in solving any particular question. We provide you solution with step by step answers. Once received solutions, you will be able to solve same kind of future problems. Tutors at TutorsGlobe have proven their excellence across the globe and a network of students are hiring tutors from each and every corner of world.
rectify the fault in fm receiver - noisy reception - first of all switch on the receiver, hearing the programme with noisy sound.
tutorsglobe.com market according to area assignment help-homework help by online classification of markets tutors
ultrasound is cyclic sound pressure along with a frequency greater than the upper limit of human hearing.
mole concept-ii tutorial all along with the key concepts of mole concept in solutions, mole concept in volumetric analysis, mole concept in electrolysis and efficiency of an electrolytic method
Lasers tutorial all along with the key concepts of Characteristics of Laser radiation, Directionality, Coherence, Emission and Absorption of Light, Stimulated Emission of Light, Absorption of Light, Elements of a Laser, Applications of Lasers
Find 24/7 online assistance of PhD tutors and History of Christianity Assignment Help now for high academic grades at viable prices.
online dat exam preparation course and online dat tutoring package offered by TutorsGlobe are the most comprehensive and customized collection of study resources on the web, offering best collection of dat practice papers, quizzes, dat test papers, and guidance.
Get well-drafted solution documents with qualified Biostatistics Assignment Help tutors at affordable prices and secure high grades easily.
Pedigree analysis tutorial all along with the key concepts of Autosome, Chromosome number, Karyotype, Homologous chromosome, Nondisjunction, Dosage compensation and Codominance
www.tutorsglobe.com offers Coding Fundamentals homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
Theory and lecture notes of Single-Peaked Preferences all along with the key concepts of economics of welfare, Benevolent Dictator, Cardinal Utility. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Single-Peaked Preferences.
TutorsGlobe.com Parametric Equations Assignment Help-Homework Help by Online Conics and Parametric Equations Tutors
www.tutorsglobe.com offers Halsey-Weir Premium Plan homework help, assignment help, case study, writing homework help, online tutoring assistance by accounting tutors.
tutorsglobe.com propagation by modified subaerial stem assignment help-homework help by online natural methods of vegetative propagation tutors
a vacuum cleaner works through creating a low pressure area in the machine causing for air at atmospheric pressure to be forced or “sucked” into the system.
1945594
Questions Asked
3689
Tutors
1460012
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!