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CBSE Class 12 Maths

Linear Programming

Each concept is a short lesson, then questions until you get three right.

0/13

13 concepts, a short lesson each

  • Graphing0/5
  • Reading figures0/2
  • Optimising0/4
  • Word problems0/2

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Boundary line from intercepts

Draw ax+by=cax + by = c through its intercepts; xa+yb=1\frac{x}{a} + \frac{y}{b} = 1

Start

Graphing0 of 5

  1. Boundary line from interceptsDraw ax+by=cax + by = c through its intercepts; xa+yb=1\frac{x}{a} + \frac{y}{b} = 1Start
  2. The half-plane testTest one point and keep its side; not the origin when the line passes through itStart
  3. The feasible regionThe overlap of every constraint, including x≥0x \ge 0 and y≥0y \ge 0Start
  4. Bounded, unbounded or emptyClassify the region before optimising: a first-quadrant region is not always boundedStart
  5. Corner pointsSolve pairs of boundary lines; drop any intersection another constraint rules outStart

Reading figures0 of 2

  1. ≥ or ≤ from the shadingPut a point from inside the shading into the line's expression; its sign fixes the inequalityStart
  2. The system behind a figureFour or five lines: eliminate options one line at a timeStart

Optimising0 of 4

  1. The corner-point methodEvaluate ZZ at every corner; the largest and smallest values are the max and minStart
  2. Minimum, negative coefficients, max − minThe minimum is not always at the origin, and the largest coordinates need not give the maximumStart
  3. Optimum over an unbounded regionThe best corner is the answer only if the half-plane Z>MZ > M (or Z<mZ < m) misses the regionStart
  4. Infinitely many optimaTwo corners tie when the objective is parallel to an edge: every point between them is optimalStart

Word problems0 of 2

  1. Formulating an LPPName the variables, write the objective, and every constraint in one unitStart
  2. Solving a word problem end to endManufacturing, diet and transport: formulate, draw the region, compare the cornersStart

Practise Linear Programming

Once the concepts click, try the questions your exam asks.

Textbook exercisesEvery exercise, with model answersPast board questionsAsked from this chapter, with solutions