Q.The corner points of the feasible solution are (0, 0), (2, 0), $\left(\dfrac{12}{7}, \dfrac{3}{7}\right)$, (0, 1). Then $Z = 7x + y$ is maximum at _______. A) (0, 0)
B) (2, 0)
C) $\left(\dfrac{12}{7}, \dfrac{3}{7}\right)$
D) (0, 1)

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 f …