A restrictive condition placed on one or more numerical or geometric variables.

The use of constraints is essential in solving linear optimization problems.


At least 150 litres of paint in total will be used to paint the classrooms in a school whose total surface area is less than 500 m². White and green paint can be used to match the school colours. According to the data provided by the decorator, the amount of green paint used should be at most 3 times the amount of white paint used. Given the characteristics of the paint, one litre of white paint covers 2 m² and costs $12, while one litre of green paint covers 3 m² and costs $15. How many litres of each colour should the decorator use to keep costs as low as possible?

The following constraints must be considered in this situation :

  • at least 150 litres of paint,
  • for a surface area of less than 500 m²,
  • 3 times more green paint than white paint.

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