The LP formulation and the underlying assumptions A prototype LP problem: The general LP formulation
A prototype LP problem:
The general LP formulation
Graphical solution of 2-var LP's Feasible Regions of Two-Var LP's The solution space of a single equality constraint The solution space of a single inequality constraint Representing the Objective Function in the LP solution space
Graphical solution of 2-var LP's
Feasible Regions of Two-Var LP's
The solution space of a single equality constraint
The solution space of a single inequality constraint
Representing the Objective Function in the LP solution space
Graphical solution of the prototype example: a 2-var LP with a unique optimal solution 2-var LP's with many optimal solutions Infeasible 2-var LP's Unbounded 2-var LP's
Graphical solution of the prototype example: a 2-var LP with a unique optimal solution
2-var LP's with many optimal solutions
Generalization to the n-var case: the ``geometry'' of the LP feasible region and the Fundamental Theorem of Linear Programming Generalization to the n-var case Polytope Convexity and Extreme Points The Fundamental Theorem of Linear Programming
Generalization to the n-var case: the ``geometry'' of the LP feasible region and the Fundamental Theorem of Linear Programming
Generalization to the n-var case
Polytope Convexity and Extreme Points
The Fundamental Theorem of Linear Programming
An algebraic characterization of the solution search space: Basic Feasible Solutions Example: LP's in ``standard form'' Basic Feasible Solutions: An algebraic characterization of extreme points for LP's in ``standard form'' Example:
An algebraic characterization of the solution search space: Basic Feasible Solutions
Basic Feasible Solutions: An algebraic characterization of extreme points for LP's in ``standard form''
The Simplex Algorithm The basic Simplex iteration through an example:
The basic Simplex iteration through an example:
