chapter 36.pdf

174 Linear Programming E3 60 174 ‘Linear Programming’ is a scientific tool to handle optimization problems. Here, we shall learn about some formulation and graphical method of solution. 6.1 Linear Inequations. (1) Graph of linear inequations ID basic concepts of linear programming problems in two va...

174 Linear Programming E3 60 174 ‘Linear Programming’ is a scientific tool to handle optimization problems. Here, we shall learn about some formulation and graphical method of solution. 6.1 Linear Inequations. (1) Graph of linear inequations ID basic concepts of linear programming problems in two variables, their applications, advantages, limitations, U (i) Linear inequation in one variable : ax  b  0, ax  b  0, cy  d  0 etc. are called linear inequations in one variable. Graph of these inequations can be drawn as follows : D YG Y x X b a O ax+b0 U Y The graph of ax  b  0 and ax  b  0 are obtained by dividing xy-plane in two semi-planes by the line ST b x   (which is parallel to y-axis). Similarly for cy  d  0 and cy  d  0. a Y cy+d>0 y X d c X cy+dc Working rule ID Y E3 X ax+by=c ax+by 0) : To draw the graph of an inequation, following procedure is followed : U (i) Write the equation ax  by  c in place of ax  by  c and ax  by  c. (ii) Make a table for the solutions of ax  by  c. D YG (iii) Now draw a line with the help of these points. This is the graph of the line ax  by  c. (iv) If the inequation is > or or