Linear Programming

Find objective function 1st

Variables are found

Z=AX+BY

Corner points

solution will be located on a corner point

If feasible region is empty, max does not exist

Unbounded

If feasible region is unbounded, only min exists

Bounded

Feasible region means it is bounded; max and min exist

Minimize or Maximize

Optimal solution should be interpreted for word problems

Graphing inequalities

Equalities

Non-negative constraints

Maximization

Standard Form

Slack variables are non negative

Corner points

Feasible solution

should not include a negative value

Non-feasible solution

Includes one negative value

Non basic variables have a zero value

Basic variables is everything else that is not a zero

Rewrite the inequality to an equality

Rewrite the objective function

Create a Simplex tableau

Pivot Element

Biggest negative value

Entering variable

Pivot element should be turned to a 1 and everything below turns to a zero

Pivot Row

Divide non-negative value in pivot column

Smallest quotient

negative elements in pivot column ='s no solution

Positive elements in pivot column ='s a solution

Exiting Variable

Slack variables

Less than or equal to

Greater than or equal to

Greater than or equal to changes to less than inequalities

No slack variables in initial matrix

Dual problem

Transpose matrix

Switch rows and columns

Dual problem created

Keep same order

Simplex Tableau

Y1,Y2,X1,X2,X3

Pivot Column

Exiting variable

Entering Variable