The Simplex Method
The Simplex Method, developed by Prof. George Dantzig, can be used to solve any LP
problem involving any number of variables and constraints.
The simplex method is the basic building block for all other methods.
Artificial Variable Techniques
A major requirement of the simplex method is the availabilityof an initial basic feasible
solution in standard form. Without it the initial simplex tableau cannot be formed. In all
the examples we dis
What is Operations Research?
Operations Research was initiated in England during the second world war, to make
scientifically based decisions regarding the best utilization of war material.
After the war, the ideas advanced in military operations were ada
Special Situations in LP
This section considers four special cases that arise in the use of the simplex method.
1. Alternative Optima
3. Unbounded solution
4. Nonexisting ( or infeasible ) solutions.
5.1 The SimplexMe
1.1The Big M Method.
This method consists of the following basic steps:
Step1: Convert the LPP into the maximization form if the problem is a minimization problem.
Step2: If any problem constraints have negative constants on the right side, multiply both
Studying the effect of changing problem parameters is known as Sensitivity Analysis.
Identifying the relatively sensitivity parameters play an important role in sensitivity analysis.
Even a small change in cert
The Graphical Method
The next step after formulation is to solve the problem mathematically to obtain the best
possible ( optimal) solution.
This lesson presents graphical solution approaches for solving any LP problem with only
2.3 Method 2: The Iso-profit (Cost) Function Line Method
According to this method, the optimal solution is found by using the slope of the
objective function line. An iso-profit (or cost) line is a collection of points that designate solutions
with the sa
1.2 Extra Variables
1.2.1 Slack Variables
We can rewrite the above product mix problem as:
Maximize = 1 + 2
1 + 32 + 3 = 9 (1 )
21 + 2 + 4 = 8 (2 )
1 , 2 , 3 , 4 0
The variables 3 and 4 are called slack variables; 3 is the unused ,i.e. slack, time on mach
MS1004 - In-Class Assignment 1
Time: One Hour
1. Reddy Mikks produces both interior and exterior paints from two row material,
M1 and M2. Following table provides the basic data of the problem.
Tons of raw material p
Linear programming is a mathematical modeling technique to optimize the usage of
Applications of Linear programming exist in the areas of military, industry,
agriculture, transportation, econom