Maths

Class 12

Maths · Class 12 · Chapter 12

Linear Programming

9 lessons 69 min 2 simulations

Linear programming finds the optimal plan when a quantity to be made as large (or as small) as possible depends linearly on two unknowns, and the unknowns are held back by a handful of linear limits. The chapter turns a word problem into three pieces: decision variables x and y, the constraints as linear inequalities with x, y ≥ 0, and the objective Z = ax + by. The inequalities cut out a feasible region, and a key fact makes the problem finite: whenever Z has a best value on that region, one of the region's corner points gives it. So the whole method is to draw the region, list its corners, and compare Z at each. The chapter then looks at the cases where this needs care: two corners that tie, a region that runs off to infinity, and constraints that no point can satisfy together.

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What the exam asks

Board papers ask for the whole graphical routine on one problem: write the constraints from the words, shade the region, find every corner by solving pairs of boundary lines, tabulate Z and state the answer, including the unbounded check when the region is open. Linear programming is not part of NEET and is not listed in the JEE Main mathematics syllabus, so this chapter matters mainly for board exams. Marks are lost on a missed corner, on a constraint written the wrong way round ("at least" is ≥, "at most" is ≤), on forgetting x, y ≥ 0, and on declaring a maximum or minimum on an unbounded region without testing the open half plane.

Lessons

9 lessons · 69 min