Playbook
Linear Programming
43 q - 1.00/paper - 5% HARD. The lowest-HARD chapter in the subject: three of its four notes pages have NEVER produced a HARD question, and both HARD ones are reading constraints off a figure. Two marks that should take under a minute. Do this first, every time.
- Questions in the bank
- 43
- q/paper (2024–25 shifts)
- 1.00
- Tagged HARD
- 5%
- Subtopics
- 4
Strand: Quick-Win
When you’ll see it
A set of linear inequalities plus something to maximise or minimise — or a feasible region to identify, classify, or read corners from.
How this chapter is tested
43 q at 1.00 per paper and 4% HARD. This is the lowest-HARD chapter in the subject by a wide margin: three of its four notes pages (/notes/mht-cet-maths/linear-programming) have NEVER produced a HARD question across the whole 44-shift bank, and the corner-point page alone is 16 q at 0%. Two marks that should take under a minute. Do this one first, every time you sit a paper.
The method does not vary. Translate the sentence into inequalities, plot the constraints, identify the feasible region, list its corner points, and evaluate the objective at each corner. The optimum of a linear objective over a convex polygon always sits at a corner, so there is nothing to search — you are comparing at most four or five numbers.
Reading constraints off a shaded region is 9 q at 22% HARD and carries the whole difficulty of the chapter — both HARD questions are figure stems with four or five boundary lines. They are answered by testing one point inside the shading against one line at a time, and by computing the sign at that point rather than trusting above/below when a coefficient is negative. Five minutes of deliberate practice, and the chapter is finished.
Because the answers are numbers produced by arithmetic at corner points, this is a chapter where checking beats guessing even under time pressure — and with no negative marking there is never a reason to leave one of these blank. One 2024 figure stem carries an official key its own working contradicts (19.8 marked where the corner gives 19.5); the bank keeps the official letter with a note.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Feasible Region — Half-Plane Tests, Bounded, Unbounded and Empty
Draw each boundary from its intercepts, choose the side with a test point (never the origin on a line through it), intersect, and classify: bounded, unbounded, or empty — the empty case is proved by adding inequalities. 13 q at 0% HARD.
Reading Constraints Off a Shaded Region
Write each boundary as x/a + y/b = 1 from its intercepts, then fix >= or <= with one interior point per line; eliminate options a line at a time. 9 q at 22% HARD — the only difficulty in the chapter.
Corner-Point Method — Maximum and Minimum of the Objective Function
Find the corners as intersections of constraint boundaries (solve the pair when neither is on an axis), evaluate the objective at each, and take the best. 14 q at 0% HARD — no question on this page has ever been rated HARD.
Formulation and Special Cases — Word Problems and Infinitely Many Optima
Turn at most, at least, and not more than into the correct inequality direction in one unit, keep x, y >= 0, and recognise the tie: an objective parallel to an edge gives infinitely many optimal points. 7 q at 0% HARD.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Optimum reported for an unbounded region
If the region is unbounded in the direction the objective improves, no maximum exists. A numeric value is still offered, and it is the largest corner value.
Corner point that fails one constraint
Two boundary lines meet at a point that lies outside the region because a third constraint excludes it. Test every candidate corner against ALL constraints before evaluating.
Inequality direction reversed
At most and at least map to opposite half-planes, and a single reversal produces a different region with entirely different corners and a clean-looking wrong answer.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Linear Programming notesDrill every linear programming question
43 questions from the bank, scoped to 4 bundled subtopics.
Drill one subtopic at a time
The 4 subtopics this playbook covers, in catalog order.
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