Question

explain why ( x geq 0 ) and ( y geq 0 ) are often constraints in linear programming problems. (2 pts)

Explanation:

In linear programming, \( x \geq 0 \) and \( y \geq 0 \) (non - negativity constraints) are often used because in most real - world applications, the variables \( x \) and \( y \) represent quantities such as the number of items produced, the amount of a resource used, etc. These quantities cannot be negative. For example, if \( x \) represents the number of cars manufactured, you can't manufacture a negative number of cars. So these constraints ensure that the solution to the linear programming problem is meaningful in the context of the real - world situation it models.

Answer:

\( x\geq0 \) and \( y\geq0 \) are non - negativity constraints. In linear programming, they are often used because the variables (like quantities of goods, resources used) typically represent real - world quantities that cannot be negative (e.g., you can't produce a negative number of items).