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+//Exa 16.4
+clc;
+clear;
+close;
+//given data :
+disp("Given the following LP model :")
+disp("minimize Z = 2*X1 + 3*X2");
+disp("subject to");
+disp("X1+X2 >= 6");
+disp("7*X1+X2 >= 14");
+disp("X1,X2 >= 0");
+disp("The introduction of non-negative constraints X1>=0 and X2>=0 will eliminate the 2nd, 3rd and 4th quadrants of XY plane.");
+disp("Compute the cordinates to plot equations relting to the constraints on the XY plane as shown below : ");
+disp("X1+X2 = 6");
+disp("When X1=0 : X2=6");
+disp("When X2=0 : X1=6");
+X1=0:6;
+X2=(6-X1);
+plot2d(X1,X2);
+disp("Consider the 2nd constraint in the form :");
+disp("7*X1+X2 = 14");
+disp("When X1=0 : X2=14");
+disp("When X2=0 : X1=2");
+X1=0:2;
+X2=(14-7*X1);
+plot2d(X1,X2);
+disp("The Optimum solution will be in any one of the corners A, B and C");
+disp("The objective function value at each of these corner points of the feasible solution space is computed as fllows by substituting its coordinates in the objective function.")
+ZA=2*0+3*14;
+ZB=2*(4/3)+3*(14/3);
+ZC=2*6+3*0;
+disp("ZA=6*0+8*0=0...
+   ZB=6*10+8*0=60...
+   ZC=6*8+8*2=64);
+disp("Since the type of the objective function is minimization, the solution corresponding to the minimum Z value should be selected as the optimum solution. The Z value is minimum for the corner point C. Hence, the corresponding solution is ");
+disp("X1 = 6  X2 = 0 and Z(Optimum) = 12");