Q.Which of the following is correct _______. A) every L.P.P. has an optimal solution
B) a L.P.P. has unique optimal solution
C) if L.P.P. has two optimal solutions then it has infinite number of optimal solutions
D) the set of all feasible solution of L.P.P. may not be convex set

The chapter proves (without proof, as a stated theorem) that when the objective function of an L.P.P. attains its optimum (maximum or minimum) value over a convex-polygon feasible region, that optimum is always attained at one of the polygon's vertices (corner points) — this is the Corner-Point or Convex-Polygon Theorem, and it is what makes the graphical method possible: instead of checking every point of an infinite region, only the (finitely many) vertices need to be checked. The Corner-Point Method proceeds in five steps: (1) convert every constraint's inequation into its boundary equation and draw the line; (2) shade the half-plane each constraint demands and locate the region common to all of them — the feasible region; (3) find every vertex of this feasible region, either by reading intercepts directly off the graph or, more reliably, by solving each relevant pair of boundary-line equations simultaneously; (4) evaluate the objective function $z$ at every vertex found; (5) the largest tabulated value of $z$ is the maximum, and the smallest is the minimum, of the objective function over the entire feasible region. If two different vertices happen to give the SAME optimal value of $z$, then (by the same convexity idea) every point on the straight segment joining those two vertices is also optimal, so the L.P.P. has infinitely many optimal solutions rather than a single unique one.