12. Linear Programming

4 topics1 h

Chapter 12 of NCERT Mathematics for Class 12: Linear Programming. Two sections — Setting the problem up and Solving it on a graph. Four videos, 1 h in all.

Worked answers to the 10 exercise questions in this chapter: Exercise 12.1

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Part 1

Setting the problem up

23 minOptimisation and the linearity that makes this class tractable, and how a stated situation becomes decision variables, constraints and an objective23 min · 16 parts

Part 2

Solving it on a graph

23 minThe feasible region as the overlap of the half planes the constraints allow23 min · 16 parts17 minWhy an optimum, if there is one, has to sit at a corner17 min · 12 parts20 minTesting every corner, and the extra check an unbounded region forces20 min · 14 parts

What you will be able to do

  • Name the larger family a linear programming problem belongs to, and say what membership of that family requires
  • Draw the line belonging to a constraint, and decide by testing one point which side of it the constraint allows
  • State the difficulty the chapter names before it introduces its two theorems, and say why an exhaustive search cannot settle it
  • Carry out the chapter's four printed steps in order on a bounded problem, and say what each step is for

What this chapter assumes you already know

  • Linear inequalities in two unknowns, solved graphically, from Class XI
  • Turning a stated condition into an inequality, with the sign pointing the way the words point
  • Forming and simplifying a linear expression in two unknowns
  • Dividing an inequality through by a positive number without disturbing it
  • A straight line from its equation, and the two points where it meets the axes
  • Systems of linear equations, and solving two of them together
  • Reading a point as an ordered pair, and the four quadrants
  • Reading a rate — rupees per item, spaces per item — as a multiplier

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "Programming means writing a computer program."
  • "Linear just means the answer comes out neat."
  • "Every optimisation problem is a linear programming problem."
  • "A letter is a letter; I do not need to say what it counts."
  • "Dividing the constraint by five hundred changes the problem."
  • "Both limits are about money."
  • "The inequality signs are obvious from the words."
  • "The objective function is one of the constraints."