Basis of a linear program
Imagine you are trying to solve a math problem. You have some rules to follow, like you can only use addition, multiplication, and subtraction. You have some variables, like "x" and "y", and you want to figure out what values of "x" and "y" will give you the answer you are looking for.
In a linear program, you have a similar situation. You have a goal you want to achieve, like make as much money as possible or use as little resources as possible. You have some rules to follow, called constraints, like you can only use a certain amount of money or resources. You also have some variables, like "x" and "y", that represent things you can change, like how much of a certain product to make or how much of a certain resource to use.
To solve the linear program, you want to find the values of the variables that will give you the best possible answer while still following all the rules (constraints). The basis of the linear program is a set of variables that are set to zero, or "basic", while the other variables are free to take on any value.
Think of it like a puzzle with some pieces that are locked in place and some pieces that you can move around. The basis is the set of locked pieces, the constraints are the rules that limit how you can move the other pieces, and the variables are the pieces you can move around.
By finding the best values for the variable pieces that you can move, while still following the rules and keeping the locked pieces in place, you can solve the puzzle and achieve your goal.
In a linear program, you have a similar situation. You have a goal you want to achieve, like make as much money as possible or use as little resources as possible. You have some rules to follow, called constraints, like you can only use a certain amount of money or resources. You also have some variables, like "x" and "y", that represent things you can change, like how much of a certain product to make or how much of a certain resource to use.
To solve the linear program, you want to find the values of the variables that will give you the best possible answer while still following all the rules (constraints). The basis of the linear program is a set of variables that are set to zero, or "basic", while the other variables are free to take on any value.
Think of it like a puzzle with some pieces that are locked in place and some pieces that you can move around. The basis is the set of locked pieces, the constraints are the rules that limit how you can move the other pieces, and the variables are the pieces you can move around.
By finding the best values for the variable pieces that you can move, while still following the rules and keeping the locked pieces in place, you can solve the puzzle and achieve your goal.