CBSE · Chapter

Linear Programming

The concepts CBSE needs, one connected idea at a time.

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CBSE · Chapter

The concepts CBSE needs, one connected idea at a time.

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Up nextBoundary line from interceptsDraw $ax + by = c$ through its intercepts; $\frac{x}{a} + \frac{y}{b} = 1$ Start

How the ideas build on each other. Each one opens once you've mastered what it needs.

Boundary line from interceptsDraw $ax + by = c$ through its intercepts; $\frac{x}{a} + \frac{y}{b} = 1$

Start

The half-plane testTest one point and keep its side; not the origin when the line passes through itLocked

The feasible regionThe overlap of every constraint, including

x \ge 0

and

y \ge 0

Locked

Bounded, unbounded or emptyClassify the region before optimising: a first-quadrant region is not always boundedLocked

Corner pointsSolve pairs of boundary lines; drop any intersection another constraint rules outLocked

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

The corner-point methodEvaluate $Z$ at every corner; the largest and smallest values are the max and minLocked
Minimum, negative coefficients, max − minThe minimum is not always at the origin, and the largest coordinates need not give the maximumLocked
Optimum over an unbounded regionThe best corner is the answer only if the half-plane $Z > M$ (or $Z < m$ ) misses the regionLocked
Infinitely many optimaTwo corners tie when the objective is parallel to an edge: every point between them is optimalLocked

Formulating an LPPName the variables, write the objective, and every constraint in one unitLocked
Solving a word problem end to endManufacturing, diet and transport: formulate, draw the region, compare the cornersLocked