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 the graph will drawn automatically of the inequalities. The graph of that inequalities is given belows.

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 belows.

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.