Q.Solve graphically: Maximize $Z = 3x + 2y$ subject to $x + y \le 6,\ 2x + y \le 10,\ x, y \ge 0$.

A two-variable LPP is solved geometrically: for each constraint $px+qy\le H$ (or $\ge$), the boundary line $px+qy=H$ is plotted via its intercepts $x=H/p,\ y=H/q$, a test point (usually the origin) decides which half-plane satisfies the inequality, and the region common to every required half-plane -- together with $x\ge0,\ y\ge0$ -- is shaded as the feasible region. Its corner points are found by solving pairs of boundary equations simultaneously; at each axis, the SMALLER …