In Mathematics, The linear programming is maximized or minimized of a linear function when subjected to various constraints(linear inequalities). We can draw any graph of inequality with the free graph drawing website www.graph2d.com. As for example, A linear programming problem is Maximize f(x,y)=3x+4y and constraints are 2x+3y<=48, x+y<=20, x>=0, y>=0. For solving this linear programming problem, type 2x+3y<=48 in the first input box, type x+y<=20 in the second input box, x>=0 in the third input box, y>=0 in the fourth input box and then press drawing button to get the graph of the inequalities. The graph of that inequalities is given bellows-

Then click on the graph of intersection point to get the co-ordinates.click on the Feasible area button to get feasible area. Again click on the graph of turning point to get the co-ordinates of turning points. The graph of that feasible area is given bellows-

we get the turning points (0,0),(20,0),(12,8),(0,16). so f(0,0)=3(0)+4(0)=0, f(20,0)=3(20)+4(0)=60, f(12,8)=3(12)+4(8)=68, f(0,16)=3(0)+4(16)=64 Hence Maximum value of f(x,y) is 68.
For learn about piecewise function of Mathematics and graphing, visit: Graphing Piecewise function of Math.