#### Linear Programming Problems Graphical Solution Procedure

Graphical Solution Procedure

The graphical solution process

1.      Take all inequality constraint as equation.

2.      Plot each equation on the graph as all of them will geometrically correspond to a straight line.

3.      Shade the possible region. Every point on the line should satisfy the equation of the line. If the inequality constraint with respect to that line is '≤' then the region under the line lying in the first quadrant is shaded. Likewise for '≥' the region above the line is shaded. The points found in the common region or area will satisfy the constraints. This common region or area is known as feasible region.

4.      Select the suitable value of Z and plot the objective function line.

5.      Draw the objective function line until the extreme points of feasible or probable region.

a.       In the case of maximization, this line will stop far from the origin and passing by at least one corner of the feasible region.

b.      In the case of minimization, this line will stop close to the origin and passing by at least one corner of the feasible region.

6.      Study the co-ordinates of the extreme points taken in step 5 and determine the maximum or minimum value of Z.

Definitions

1.      Solution - is defined as any specification of the values for decision variable among (x1, x2... xn).

2.      Infeasible solution - a solution for which at least one constraint is not fulfilled.

3.      Feasible solution - a solution for which all constraints are fulfilled or satisfied.

4.      Optimal solution is a feasible solution or explanation that has the best favorable value of the objective function.

5.      Feasible region is a collection or group of all feasible solutions.

6.      Multiple optimal solution - refers to more than one solution with the similar optimal value of the objective function.

7.      Most favorable value - is the biggest value if the objective function is to be maximized, while it is the minimum if the objective function is to be minimized.

8.      Feasible region - The region contains all the solutions of an inequality

9.      Unbounded solution - If the value of the objective function can be raised or reduced indefinitely such solutions are known as unbounded solution.

10.  Corner point feasible solution - a solution that stays at the corner of the feasible region.

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