Playbook
Linear Programming
46 q - 1.00/paper - 4% HARD. The lowest-HARD chapter in the subject, and one of its two subtopics (Objective Function, 23 q) has NEVER produced a HARD question. Two marks that should take under a minute. Do this first, every time.
- Questions in the bank
- 46
- q/paper (2024–25 shifts)
- 1.00
- Tagged HARD
- 4%
- Subtopics
- 2
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
46 q at 1.00 per paper and 4% HARD. This is the lowest-HARD chapter in the subject by a wide margin, and one of its two subtopics — Objective Function, Maximisation and Minimisation, 23 q — has NEVER produced a HARD question across the whole 45-shift bank. 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.
Feasible Region — Identification, Constraints, Classification is 23 q at 9% HARD and carries whatever difficulty the chapter has. The questions that misbehave are the ones about the region itself: whether it is bounded, whether it is empty, which half-plane a given inequality selects. Those are worth five minutes of deliberate practice, and then 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.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Translating constraints into inequalities
Turn at most, at least, and not more than into the correct inequality direction, and never forget the non-negativity constraints that the wording leaves implicit.
Plotting and identifying the feasible region
Draw each boundary line, choose the correct half-plane with a test point, and take the intersection. 23 q at 9% HARD across this subtopic — the only place difficulty appears in this chapter.
Classifying the region — bounded, unbounded, empty
An unbounded region may have a minimum and no maximum, or the reverse; an empty region has no solution at all. Recognising which case you are in is what separates the 9% HARD questions from the rest.
Evaluating the objective at corner points
Find the corners as intersections of constraint boundaries, evaluate the objective at each, and take the best. 23 q at 0% HARD — no question in this subtopic has ever been rated 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.
Drill every linear programming question
46 questions from the bank, scoped to 2 bundled subtopics.
Drill one subtopic at a time
The 2 subtopics this playbook covers, in catalog order.
Related playbooks
Often paired with this one — the technique, the trap or the taxonomy overlaps. Drill these next.