GRAPHICAL METHOD LINEAR PROGRAMMING

linear programming

solving problems where quantity maximized/minimized when subject x is constrained

when does linear programming arise

available sources limited/not used completely

history of linear programming

american math during ww2 to ship resources

proportionality assumption

variable x and y proportional to value obtained

additivity assumption

x + y must = sum

divisibility assumption

real numerical value

constraint assumption

constraints cant change

feasible region

where all inequalities overlap

feasible region

where all inequalities overlap

properties of linear programming model

1. linear relationship beteeen variables, constraints (written as inequalities)

2. requires objective (maximize, minimize)

3. structural constraint

4. constraints cant be negative (x, y >= 0)

assumptions of linear program model (padc)

1. proportionality

2. additivity

3. divisibility

4. certainty

ways to solve linear progeam model

1. graphical (2-3 variables)

2. simplex (any # variables)

how to find minimized value

• use vertices given (feasible point)

• at the feasible point only like where all graphs meet

how to do graphical method

1. find variables

2. find all equations possible (as inequalities)

3. graph all points and find feasible region

4. find area that actually fits all equations and the points that surround them = feasible points

5. if there are any overlaps in the feasible point area then solve for it (system of equations)

6. plug feasible points and any overlaps into general equation