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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. You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

## Glossary

### graph

A diagram showing a relationship between two variables.
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.

Full Glossary List

## This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)D1Linear programmingLinear programming-
AQA AS Further Maths 2017Discrete MathsLinear ProgrammingLinear Programming-
AQA AS/A2 Further Maths 2017Discrete MathsLinear ProgrammingLinear Programming-
CBSE XII (India)Linear-ProgrammingLinear-ProgrammingTerminology: constraints, objective function, optimization-
Edexcel A-Level (UK - Pre-2017)D1Linear programmingLinear programming-
Edexcel AS Further Maths 2017Decision Maths 1Linear ProgrammingLinear Programming-
Edexcel AS/A2 Further Maths 2017Decision Maths 1Linear ProgrammingLinear Programming-
OCR A-Level (UK - Pre-2017)D1Linear programmingLinear programming-
OCR AS Further Maths 2017Discrete MathsGraphical Linear ProgrammingLinear Programming-
OCR MEI AS Further Maths 2017Modelling with AlgorithmsLinear ProgrammingLinear Programming-
OCR-MEI A-Level (UK - Pre-2017)D1Linear programmingLinear programming-
Universal (all site questions)LLinear programmingLinear programming-