MHT-CET Maths · Free notes
Linear Programming — MHT-CET Maths
Linear Programming is the cheapest chapter in MHT-CET Maths and one question a paper: barely one in thirty of its past-year questions is HARD, and the method never changes. Draw each boundary line, pick the correct side with a test point, take the intersection, list the corner points, and evaluate the objective at each corner — the optimum of a linear function over a polygon always sits at a corner, so there is nothing to search. The pages below follow that order. The only place difficulty appears is the figure questions, where a shaded region is given and the constraints must be read off it; both HARD questions in the chapter are of that kind, and they are answered by testing one point inside the region against one line at a time. The last page collects the word-problem formulations and the single trick worth knowing — when the objective is parallel to an edge, the optimum is a whole segment, so 'infinitely many solutions' is a real answer. Every PYQ is tagged.
The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.
Subtopic notes
Feasible Region — Half-Plane Tests, Bounded, Unbounded and Empty
16 PYQsEach linear inequality keeps one side of its boundary line; the feasible region is the intersection of those half-planes, and it can be a bounded polygon, an unbounded region, or nothing at all.
Reading Constraints Off a Shaded Region
11 PYQsGiven a shaded region, recover its inequalities: write each boundary line from its intercepts, then pick a point inside the shading and test it against each line to fix ≥ or ≤.
Corner-Point Method — Maximum and Minimum of the Objective Function
28 PYQsA linear objective over a polygon takes its maximum and minimum at corners: list the vertices, evaluate Z at each, and read off the largest and smallest.
Formulation and Special Cases — Word Problems and Infinitely Many Optima
14 PYQsTurn a word problem into variables, an objective and inequalities in consistent units; and recognise the tie — when two adjacent corners give the same optimum, every point of the edge between them is optimal.
Formula & revision sheet
12 formulas · 12 gotchas across all subtopics — the exam-eve cheat-sheet
Formula & revision sheet
12 formulas · 12 gotchas across all subtopics — the exam-eve cheat-sheet
Formulas (3)
Watch out for (3)
- Testing the origin on a line through it→ The Half-Plane Test: Draw the Line, Test a Point, Keep One Side
- Calling every first-quadrant region bounded→ Bounded, Unbounded or Empty: Classify Before You Optimise
- Keeping an intersection that a third constraint kills→ Vertices of the Region: Intersect Pairs of Boundaries, Then Check the Rest
Formulas (3)
Watch out for (3)
- Swapping the intercepts→ The Boundary Line From Its Intercepts: x/a + y/b = 1
- Testing a point on the boundary→ Fix ≥ or ≤ With One Point Inside the Shading
- 'Above the line' read as ≥ when a coefficient is negative→ Four or Five Lines: Eliminate Options One Line at a Time
Formulas (4)
- The Corner-Point Theorem: Evaluate Z at Every Vertex · Corner-point method
- Corners That Are Not on the Axes: Solve the Pair of Lines · Corner from two boundaries
- Minimising, Negative Coefficients, and Max Minus Min · Max minus min
- When the Figure Labels the Corners: Read Coordinates, Then Substitute · Figure stems
Watch out for (4)
- Stopping at the first good corner→ The Corner-Point Theorem: Evaluate Z at Every Vertex
- Assuming the fractional corner is the answer→ Corners That Are Not on the Axes: Solve the Pair of Lines
- Treating the largest coordinates as the maximum→ Minimising, Negative Coefficients, and Max Minus Min
- Reading a corner one grid unit off→ When the Figure Labels the Corners: Read Coordinates, Then Substitute
Formulas (2)
Watch out for (2)
- Mixing hours and minutes→ Formulating an LPP: Variables, Objective, Constraints in One Unit
- Answering 'two distinct points'→ Infinitely Many Optima: The Objective Parallel to an Edge
PYQ weightage by concept
12 concepts · 69 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
12 concepts · 69 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| The Half-Plane Test: Draw the Line, Test a Point, Keep One Side | 6 | 9% |
| Bounded, Unbounded or Empty: Classify Before You Optimise | 4 | 6% |
| Vertices of the Region: Intersect Pairs of Boundaries, Then Check the Rest | 3 | 4% |
| Concept | PYQs | Share |
|---|---|---|
| The Boundary Line From Its Intercepts: x/a + y/b = 1 | 3 | 4% |
| Fix ≥ or ≤ With One Point Inside the Shading | 3 | 4% |
| Four or Five Lines: Eliminate Options One Line at a Time | 3 | 4% |
| Concept | PYQs | Share |
|---|---|---|
| The Corner-Point Theorem: Evaluate Z at Every Vertex | 6 | 9% |
| When the Figure Labels the Corners: Read Coordinates, Then Substitute | 4 | 6% |
| Corners That Are Not on the Axes: Solve the Pair of Lines | 2 | 3% |
| Minimising, Negative Coefficients, and Max Minus Min | 2 | 3% |
| Concept | PYQs | Share |
|---|---|---|
| Infinitely Many Optima: The Objective Parallel to an Edge | 5 | 7% |
| Formulating an LPP: Variables, Objective, Constraints in One Unit | 2 | 3% |
Test yourself on Linear Programming
15 past MHT-CET questions from this chapter, timed at 27 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.