This diagram shows how the optimum value of a quantity Q = ax+by can be found from a linear programming graph. First the constraints are plotted to create an unshaded region within which solutions must occur.

Graphs of Q=ax+by are plotted for various values of Q and can be used to help identify the values of x and y that give the required values of Q.

Graphs of Q=ax+by are plotted for various values of Q and can be used to help identify the values of x and y that give the required values of Q.

## Software/Applets used on this page

## Glossary

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### linear

Straight, not curved. A linear equation is of the first degree, for example y = 2x+1.

### union

The union of two sets A and B is the set containing all the elements of A and B.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic |
---|---|---|---|

AQA A-Level (UK - Pre-2017) | D1 | Linear programming | Linear programming |

AQA AS Further Maths 2017 | Discrete Maths | Linear Programming | Linear Programming |

AQA AS/A2 Further Maths 2017 | Discrete Maths | Linear Programming | Linear Programming |

CBSE XII (India) | Linear-Programming | Linear-Programming | Terminology: constraints, objective function, optimization |

Edexcel A-Level (UK - Pre-2017) | D1 | Linear programming | Linear programming |

Edexcel AS Further Maths 2017 | Decision Maths 1 | Linear Programming | Linear Programming |

Edexcel AS/A2 Further Maths 2017 | Decision Maths 1 | Linear Programming | Linear Programming |

OCR A-Level (UK - Pre-2017) | D1 | Linear programming | Linear programming |

OCR AS Further Maths 2017 | Discrete Maths | Graphical Linear Programming | Linear Programming |

OCR MEI AS Further Maths 2017 | Modelling with Algorithms | Linear Programming | Linear Programming |

OCR-MEI A-Level (UK - Pre-2017) | D1 | Linear programming | Linear programming |

Universal (all site questions) | L | Linear programming | Linear programming |