Geometric Method

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

Graph conditions to find feasible region

Identify the feasible area; Is it bounded or unbounded?

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

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

Minimizing - solution is the smallest value

Maximization - solution is the largest value

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

Slack Variables for Maximization problems are represented by (s)

Slack Variables for Minimization problems are represented by (x)

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

Enter Pivot

Exit Pivot

Basic

Non Basic

Maximize

Minimize

Transpose (Columns become rows)

Problem turns into a maximization problem

Set Up Tableau

Rewrite equations using Y

Row Operations are performed to set pivot exit element to 1

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

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

Solution is identified

Maximization - solution is the largest value

Minimization - solution is the smalles value

Simplex Method

Linear Programming

Graphing Inequalities

Slope M = y2–y1/ x2 -x1

Slope Intercept Form y = mx + b

Standard form ax + bx = c

Shade Above = greater than or equal to

Shade Below = less than or equal to

Horizontal Line x = 0

Vertical Line x = 0

Create Tableau

Feasible Region = where everything works

Unbounded = not contained

Bounded = trapped between lines

Table Method