Within or on the boundary of the space ABCDEFis feasible. Interactively with graphing the constraints one at a time, so you can see howР”В®ach constraint affects the solution space.Р”Р‡easible space in Figure 2.1 is delineated by the line segments joining the In the output screen, you will be able to experiment Is illustrated with the constraint 6x 1 + 4x 2 Satisfies the inequality, then the side in which it lies is the Into two half-spaces, one on each side of the graphed line. All it does is divide the (x 1, x 2)-plane

Thus, the line passes through the two points (0,6)Р”Р„nd (4,0), as shown by line (1) in Figure 2.1.Р”В¬onsider the effect of the inequality. For example, after replacing 6x 1 + 4x 2 = 24 with the straight line 6x 1 + 4x 2 = 24, weР”В¬an determine two distinct points by first setting x 1 = 0 to obtain x 2 = 24/4= 6 and then setting x 2 = 0 to obtain Lies above the x l-axis and to the right of the x 2- axis.Р”Р„ccount for the remaining four constraints, first replace each inequality withР”Р„n equation and then graph the resulting straight line by locating two distinct Of the variables restricts the solution-space area to the first quadrant that The exterior- and interior-paint variables, respectively. In FigureР”Сћ.1, the horizontal axis x 1 and the vertical axis x 2 represent Procedure uses two examples to show how maximization and minimization objectiveР”В®xample solves the Reddy Mikks model of Example 2.1-1.Р”Р„ccount for the nonnegativity constraints x1>= 0 and x2>=0. Determination of the optimum solution from amongР”Р„ll the feasible points in the solution space. Determination of the feasible solution space.Р”Сћ. Thus, the simplex algorithm is efficient since it considers few feasible solutions, provided by the corner points, to determine the optimal solution to the linear programming problem.1.

The decision variables in the linear programming problem should be non-negative.

In case, any linear programming problem has a negative resource value, then it should be converted into positive value by multiplying both the sides of constraint inequality by РІР‚Сљ-1РІР‚Сњ.

The right-hand side of each constraint inequality should be non-negative.

This procedure of substitution of variable value continues until any further improvement in the value of the objective function is possible.Р”Р‡ollowing two conditions need to be met before applying the simplex method: Thus, the value of the objective function gets improved through this method. The decision maker will enter appropriate values of the variables in the problem and find out the variable value that contributes maximum to the objective function and removes those values which give undesirable results. The value of decision variables is taken as zero since the evaluation in terms of the graphical approach begins with the origin. The iterative process begins by assigning values to these defined variables. In other words, the simplex algorithm is an iterative procedure carried systematically to determine the optimal solution from the set of feasible solutions.Р”Р‡irstly, to apply the simplex method, appropriate variables are introduced in the linear programming problem, and the primary or the decision variables are equated to zero.

The Simplex Method or Simplex AlgorithmР’В is used for calculating the optimal solution to the linear programming problem. The optimal solution is and with an optimal value that represents the workshopРІР‚в„ўs profit. The green colored areaР’В corresponds to the set of feasible solutions and the level curve of the objective function that passes by the optimal vertex is shown with a red dotted line. The constraints represent the number of hours available weekly for machines A, B and C, respectively, and also incorporate the non-negativity conditions.Р”Р‡or the graphical solution of this model we will use the Graphic Linear Optimizer (GLP)Р’В software.

: Product 2 Units to be produced weekly.: Product 1 Units to be produced weekly.The profit of each product per unit soldР”Р‡ormulate and solve using the graphical method a Linear Programming model for the previous situation that allows the workshop to obtain maximum gains.The total available hours for each machine, per week.The hours needed at each machine, per product unit.The Graphical MethodР’В ( graphic solving) is an excellent alternative for the representation and solving of Linear Programming models that have twoР’В decision variables.Р”В®xercise #1:Р’В A workshop has three (3) types of machines A, B and C it can manufacture two (2) products 1 and 2, and all products have to go to each machine and each one goes in the same order First to the machine A, then to B and then to C.

Graphic lp optimizer