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I'm working on an optimization problem that and I am having trouble figuring out how to set up some of the constraints required.

To make it easier for me to explain, I'm going to describe a scenario that closely matches the problem I am facing: Let's assume I am organizing a karate tournament and 100 people enter. Those 100 people have skill levels that are uniformly distributed across the type of belt they wear with Black belts being the most skilled.

Belt Skill Level: Black > Red > Brown > Purple > Blue > Green > Orange > Yellow > White

For this tournament, I want no more than 10% of contestants to have White belts, no more than 20% of contestants to have Yellow OR White Belts, no more than 30% of contestants to have Orange Or Yellow or White belts, ... , and no more than 95% of contestants to have a Red Belt or below (implying I want at least 5% of entrants to have a black belt).

My question to stack exchange is how do I go about setting up a constraint like this? This just happens to be one piece of a larger problem that I am trying to solve using Python.

Thanks for the help!

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    It is unclear what you are choosing in your optimization and hence what to put the constraints on. – 2017-02-24
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    Let me add some more to the problem. Let's also add that there is an entrant fee that is higher the less skilled you are. As the organizer I want to maximize the entrance fee to the tournament. A white belt may have an entrance fee of 90− 100 while a yellow belt may have a fee of 85−96. – 2017-02-24

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A conjunction of inequality constraints like this?

(White <= 10) and 
((White + Yellow) <= 20) and 
((While + Yellow + Orange) <= 30) and 
((White + Yellow + Orange + Green) <= 40) and 
((White + Yellow + Orange + Green + Blue) <= 50) and 
((White + Yellow + Orange + Green + Blue + Purple) <= 60) and 
((White + Yellow + Orange + Green + Blue + Purple + Brown) <= 70) and 
((White + Yellow + Orange + Green + Blue + Purple + Brown + Red) <= 95)

As pointed out by @Jan: apart from the constraints, an optimization typically involves some criterion (figure of merit) to maximize or minimize.

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    My apologies Axel - let me add some more to the problem. Let's also add that there is an entrant fee that is higher the less skilled you are. As the organizer I want to maximize the entrance fee to the tournament. A white belt may have an entrance fee of $ 90-$ 100 while a yellow belt may have a fee of $ 85-$ 96. – 2017-02-24