Problem Solving Skills for Students

In this Video, Dr. Sanjay Biyani, Academic Director and Dr. Neeta Maheshawari, discuss the challenges faced by students while solving Linear Programming Problems. According to Dr. Neeta Maheshawari, one should follow following steps in order to solve the LPP:
Problem formulation
Read the Problem
Understand the Requirements / Objective
Solve the Problems with the available data forming equations
They have also discussed the concept of Slack Variable and Artificial Variable According to Dr. Neeta Maheshawari In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it to equality. Introducing a slack variable replaces an inequality constraint with an equality constraint and a non negativity constraint and an artificial variable is used for equality constraints and for greater-than or equal inequality constraints.
Dr. Sanjay Biyani suggested that while solving LPP first object function is defined than Constraints are defined and while defining constraints function our objective should be to utilize minimum resource in an optimum manner.
She said that to convert inequality into equality if there is less than sign slack variable are used and if there is greater than sign then artificial variables are used Slack variable has positive nature and its value is zero, so values used are zero, S1 and S2. Artificial variable has negative nature and its value is infinite that’s why we use negative M for the same.
On being asked by Dr. Sanjay Biyani, that why do we associate M with artificial variable and what is the object behind this, Dr. Neeta Maheshawari replied that The Big-M method of handling instances with artificial variables is the “commonsense approach”. The object is to convert inequality into equality and to arrange proportion into harmonically relationship.
Dr. Sanjay Biyani inferred that when we associate M value with Artificial Variable then possibility of coming the variable in final table is completely reduced, that is, if M is associated with Artificial Variable, the same will never appear in final simplex table.
More Detail:-