NCERT Mathematics, Class 12, textbook pages 394–405 (Part II)

How to help your child with Class 12 Maths Chapter 12, Linear Programming, at home

Optimising under constraints, explained for parents: a 60-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

corners: (0,0), (4,0), (0,4)max Z at a corner

NCERT Class 12 Maths Chapter 12 Linear Programming: what it teaches

Your teen forms linear programming problems from real situations, graphs the feasible region from inequalities, and finds the maximum or minimum of an objective function at corner points.

Why it matters later. Linear programming is used in business, logistics and operations research.

See it: this chapter in pictures

maximise Z = 50x + 30ysubject to constraintsx, y ≥ 0
Objective plus constraints.
corners: (0,0), (4,0), (0,4)max Z at a corner
The optimum is at a corner.
corners: (0,0), (4,0), (0,4)Z = 0, 12, 8max Z = 12 at (4, 0)
Compare Z at each corner.

You need

  • graph paper
  • coloured pencils
  • a calculator

Tonight’s 60 minutes

  1. A baker makes cakes (₹50 profit) and biscuits (₹30) with limited flour and time. Write constraints.
  2. Graph the feasible region.
  3. List corner points.
  4. Evaluate profit at each corner and pick the best.

Words to use

  • objective function
  • constraint
  • feasible region
  • corner point
  • optimal solution

Watch for

  • Missing non-negativity constraints. Always include x ≥ 0, y ≥ 0.
  • Evaluating random points. Only corner points of the feasible region.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouZ = 3x + 2y, corners (0,0), (4,0), (0,4)?

Your childZ = 0, 12, 8: max 12 at (4, 0).

A game for this week: Profit planner

  1. Invent a small business with two products.
  2. Write constraints and profit.
  3. Graph and find the best plan.
  4. Present the decision.

A 5-day plan, 60 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Factory planning.
  • Diet planning.
  • Delivery routes.
  • Budget allocation.

Quick check

Ask these at the end of the week. Tap to see the answer.

Where does the optimum occur?

At a corner point of the feasible region.

Maximise Z = 3x + 2y with x + y ≤ 4, x, y ≥ 0?

12 at (4, 0).

What is a feasible region?

The set of points satisfying all constraints.

Ready for the next chapter when your child…

  • Formulates LPPs.
  • Graphs feasible regions.
  • Finds optimal solutions at corners.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 12). See the full Class 12 parent guide for every chapter.

Questions parents ask

Why check only corners?

A linear objective reaches its best value at a vertex.

What if the region is unbounded?

The optimum may not exist; check carefully.

Where is LP used?

Production planning, diets, transport.