## An optimal, as well as feasible solution to an LP problem is obtained by choosing from several values of x1,x2,.....,xn, the one set of values that satisfies the given set of constraints simultaneously and also provides the optimal [maximum or minimum] value of the given objective function.                                                                                                                                                        For LP problems that have only two variables, it is possible that the entire set of feasible solutions can be displayed graphically by plotting linear constraints on a graph paper to locate the best [optimal] solution. The technique used to identify the optimal solution is called a graphical solution approach or technique for an LP problem with two variables.                                                                      Although most real-world problems have more than two decision variables, and hence cannot be solved graphically, this solution approach provides a valuable understanding of how to solve LP problems involving more than two variables algebraically.                                                                                                   In this chapter, we shall discuss two graphical solution methods or approaches (i) Extreme point solution method (ii) Iso-profit (cost) function line method to find the optimal solution to an LP problem.

### Intersection of subring

How to prove the intersection of two subrings is a subring? Let S1 and S2  be two subrings of a ring R. Then S1∩S2 is not empty since ...