Geometric Method

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Table Method

Feasible Region = where everything works

Bounded = trapped between lines

Unbounded = not contained

Create Tableau

Graphing Inequalities

Vertical Line x = 0

Horizontal Line x = 0

Shade Below = less than or equal to

Shade Above = greater than or equal to

Standard form ax + bx = c

Slope Intercept Form y = mx + b

Slope M = y2–y1/ x2 -x1

Linear Programming

Simplex Method

Solution is identified

Minimization - solution is the smalles value

Continue to perform row operations until there are no other negatives in the last row

Continue to perform row operations to set the value above and below the exit pivot to 0

Row Operations are performed to set pivot exit element to 1

Rewrite equations using Y

Set Up Tableau

Problem turns into a maximization problem

Transpose (Columns become rows)

Minimize

Maximize

Identify Pivot Elements; Entering pivot is column with most negative in last row; Exit pivot is the smallest value product of last row divided by enter column

Non Basic

Basic

Exit Pivot

Enter Pivot

Slack Variables are used to "pick up slack" on the left & right hand side of the equations

Slack Variables for Minimization problems are represented by (x)

Slack Variables for Maximization problems are represented by (s)

Solution is determined; point in the feasible area that maximizes or minimizes the objective function

Maximization - solution is the largest value

Minimizing - solution is the smallest value

Create a table with the corner point coordinates and insert coordinates to solve for the objection function

Identify the feasible area; Is it bounded or unbounded?

Graph conditions to find feasible region

Maximizing or minimizing a linear objective function subject to constraints (conditions

Geometric Method