Chapter 4.13, Problem 2P

Program Plan Intro

Linear programming (LP):

• The linear programming(LP) is also known as linear optimization.
• Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.
• The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.
• More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.

Phase 1 in LP:

• In phase 1, the first step is to multiply both sides of a constraints with “-1” to turn the “$\ge$” constraints to “$\le$” constraints. In this phase itself, one more step included is multiply the inequality with “-1” if the right side of the inequality is negative.
• If the right side of a “$\le$” constraints is negative, then subtract the artificial variable “$a_0$” from its left side.
• The artificial variables for the equality constraints are “$a_0$” and slack variables. The artificial variable should be 0.
• The user need a Phase I if the initial basic solution is not feasible. The user can begin Phase II otherwise.