There are eight steps to solving a linear programming problem graphically: 1) Formulate the problem by translating it into mathematical equations representing the objective function and constraints, 2) Draw the constraint lines by connecting the intercepts of each constraint equation, 3) Determine the feasible solution region by checking if the origin satisfies each constraint, 4) Plot the objective function lines to determine the direction of improvement, 5) The optimal solution occurs at the corner of the feasible region that is furthest in the direction of improvement.

1. Steps in solving an LP Problem
graphically

2.  There are eight steps are involved in solving
a problem.

3.  Formulation refers to translating the real
world problem into a format of mathematical
equations
 that represent the objective function.
 Thorough understanding of the problem is
necessary.

4.  Constraint lines represent the limitations on
available resources.
 Constraint lines are drawn by connecting the
horizontal and vertical intercepts found from
f each constraint equation.

5.  Plug in the coordinates of the origin (0,0)
 If it satisfies the constraint, then all points
on the origin side of the line are feasible.
 If it does not satisfy the constraint ,then all
points on the other side and away from the
origin are feasible.

6.  The feasible solution region represents the
area on the graph that is valid for all
constraints.
 Choosing any point in this area will result in
a valid solution.

7.  Plot two objective function lines to
determine
the direction of improvement.

8.  Optimal solutions always occur at corners.
 The most attractive corner is the last point
in the feasible solution region

9.  Determine the optimal solution by
algebraically calculating coordinates of the
most attractive corner.