Категории: Все - inequality - variables - objective

по Reina P. Castro 3 лет назад

590

Linear Programming

Linear programming is a mathematical method used to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. The Simplex method is a popular algorithm for solving linear programming problems.

Linear Programming

Linear Programming

Minimization

Entering Variable
Exiting variable
Pivot Column
Y1,Y2,X1,X2,X3
Simplex Tableau
Transpose matrix
Keep same order
Dual problem created
Switch rows and columns
Dual problem
No slack variables in initial matrix
Greater than or equal to
Greater than or equal to changes to less than inequalities

Simplex Method

Less than or equal to
Slack variables
Exiting Variable
Pivot Row
Divide non-negative value in pivot column

Positive elements in pivot column ='s a solution

negative elements in pivot column ='s no solution

Smallest quotient

Pivot Element
Pivot element should be turned to a 1 and everything below turns to a zero
Biggest negative value

Entering variable

Create a Simplex tableau
Rewrite the objective function
Rewrite the inequality to an equality

Table Method

Basic variables is everything else that is not a zero
Non basic variables have a zero value
Non-feasible solution

Includes one negative value

Feasible solution

should not include a negative value

Slack variables are non negative
Standard Form
Maximization
Non-negative constraints
Equalities

Graphing Method

Graphing inequalities
Optimal solution should be interpreted for word problems
Minimize or Maximize
Corner points
solution will be located on a corner point

Bounded

Feasible region means it is bounded; max and min exist

Unbounded

If feasible region is unbounded, only min exists

If feasible region is empty, max does not exist

Z=AX+BY
Find objective function 1st
Variables are found