Dual linear program

So, imagine you have a bunch of toys and you want to give them to your friends. You want to be fair and give everyone a fair share. But, you also want to make sure you don't run out of toys before everyone gets one.

Now, let's say each friend has a certain value or importance to you, and you want to give them more toys based on their value. How do you figure out how many toys to give to each friend to make them happy but also not run out of toys?

This is where a dual linear program comes in. It's like a game where you have two teams, one that's trying to give out toys and another that's trying to get the most toys possible. The first team has to make sure they give out enough toys to make everyone happy, while the second team has to try to get as many toys as possible while still being fair.

To make this game work, we use some fancy math called linear programming. This helps us figure out how many toys to give to each friend based on their value and how many toys we have. It's like creating a recipe for how to give out toys.

The dual part of the program is like having two games going on at once. One game is the normal game where you're trying to give out toys fairly. The other game is like a mirror version of the first game, where you're trying to maximize the number of toys you get while still being fair.

By playing both games at the same time, we can make sure everyone gets a fair share of toys and we don't run out of toys before everyone gets one. So, we all get to have fun and play with toys!