Linear programming asks for no clever insight. Read the problem, write the constraints, draw the region, find the corner points, evaluate the objective function at each, state the answer. The method is identical every time, the question types barely vary, and the marks are reliable — which makes leaving it until the final week a genuinely poor trade.
| Class | 12 |
|---|---|
| Subject | Maths |
| Character | Mechanical and highly predictable |
| The method | Same five steps every question |
| Board | CBSE, ISC |
The five steps, unchanging
- Define the variables explicitly, in words. Marks are awarded for this and students skip straight to the inequalities.
- Write the constraints, including the non-negativity conditions. Forgetting those is the most common single omission.
- Draw the feasible region, shaded clearly, on ruled axes with a stated scale.
- Find the corner points, solving simultaneously where lines intersect rather than reading them off approximately.
- Evaluate the objective function at each corner and state the maximum or minimum in a sentence that answers the original question.
Corner points read off the graph rather than solved algebraically are the main source of lost marks. A graph is a guide; the coordinates come from solving the two equations. Students who eyeball an intersection at (3, 4) when it is actually (3.2, 3.6) lose the whole evaluation.
The presentation that carries marks
A ruled graph with the axes labelled, the scale stated, each constraint line labelled, and the feasible region shaded unambiguously. This is not decoration — it is where a large share of the credit sits, and a rough sketch cannot earn it.
The final answer must also return to the words of the question. "Maximum profit is 380 when 4 of A and 6 of B are produced" earns the last mark; the number alone does not.
Why students leave it late
Because it looks easy and therefore skippable, and because it usually sits near the end of the textbook. Both are reasons it gets a rushed hour in February rather than a proper two sessions in October, and a rushed hour is not enough to build the graph discipline the marks depend on.
How much practice it needs
Six or eight full questions, done properly with ruled graphs, is genuinely enough for most students. That is a small investment for a predictable return, and it is the strongest argument for doing it early rather than last.
Questions parents ask
Is it really that predictable?
The method does not vary and the question types are limited — manufacturing, diet, transport style problems. Practising a handful covers most of what appears.
Does the graph have to be on graph paper?
It should be ruled, scaled and clearly labelled. Follow whatever the board requires for your child’s session, but never freehand.
Can the corner points be read from the graph?
They should be confirmed algebraically. Reading them off is where the marks go.
How early should it be covered?
Whenever it fits — it does not depend on other chapters. That independence is a reason to do it early and bank the marks.