Graphical Method of Solution of a Linear Programming ProblemSo far we have learnt how to construct a mathematical model for a linearprogramming problem. If we can find the values of the decision variables x1, x2, x3,..... xn, which can optimize (maximize or minimize) the objective function Z, thenwe say that these values of xi are the optimal solution of the Linear Program (LP).The graphical method is applicable to solve the LPP involving two decisionvariables x1, and x2, we usually take these decision variables as x, y instead of x1,x2. To solve an LP, the graphical method includes two major steps.a) The determination of the solution space that defines the feasible solution. Notethat the set of values of the variable x1, x2, x3,....xn which satisfy all the constraintsand also the non-negative conditions is called the feasible solution of the LP.b) The determination of the optimal solution from the feasible region.a) To determine the feasible solution of an LP, we have the following steps.Step 1: Since the two decision variable x and y are non-negative, consider onlythe first quadrant of xy-coordinate planeDraw the line ax + by = c(1)For each constraint,the line (1) divides the first quadrant in to two regions say R1 and R2, suppose (x1,0) is a point in R1. If this point satisfies the in equation ax + by c or ( c), thenshade the region R1. If (x1, 0) does not satisfy the inequality, shade the region R2.Step 3: Corresponding to each constant ...
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