Ch 12 introduces linear programming — an optimisation technique for problems with linear constraints. Students formulate real-world problems and solve them graphically using the corner point method.
Define decision variables, write the objective function (maximise/minimise Z = ax + by), and express constraints as linear inequalities including non-negativity (x, y ≥ 0).
Graph each constraint to get the feasible region (intersection of all half-planes). Evaluate the objective function at each corner point (vertex) of the feasible region. The optimal value occurs at a corner point.
Download: https://ncert.nic.in/textbook/pdf/lemh206.pdf | Complete book Part II: https://ncert.nic.in/textbook/pdf/lemh2ps.zip
If the optimal value of the objective function exists for a bounded feasible region, it occurs at one of the corner points (vertices). For an unbounded region, the optimal may or may not exist, and additional checks are needed.
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