Linear Programming

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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