Cheat sheet · Class 12 · CBSE · Commerce Mathematics
Linear Programming cheat sheet
The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.
CBSE Class 12 · Mathematics
Cheat sheet
Chapter 12Linear Programming
Optimum lies at a corner point of the feasible region.
1. Terms
- Objective function Z = ax + by (maximise / minimise).
- Constraints: linear inequalities; x, y ≥ 0.
- Feasible region: points satisfying all constraints.
2. Corner Point Method
- Graph the constraints and shade the feasible region.
- Find all corner points.
- Evaluate Z at each corner.
- Bounded region: max and min exist among corners.
- Unbounded: check with an extra inequality (Z > max or Z < min).
3. Key Points
- Types: manufacturing, diet, transportation problems.
- Infeasible: no common region.
- Multiple optimal: two corners give the same value.
- Always state units in the answer.
Remember: Z, constraints | corner point method | unbounded check
Linear Programming: questions and notes
More Class 12 · CBSE · Commerce Mathematics cheat sheets
Practise Linear Programming
Sign up free to practise the full chapter. Questions you get wrong come back until you've mastered them.
Start practising freeFree to start · No credit card needed