# What are basic and nonbasic variables in linear programming?

**basic variables**can be defined as the m

**variables**which can take any value other than zero. Moreover, if the

**variables**satisfy the non-negativity condition of the LP model, the

**basic**solution created by them is called the

**basic**feasible solution. The remaining

**variables**are known as the

**non-basic variables**.

Furthermore, what are basis variables?

A **variable** is a **basic variable** if it corresponds to a pivot column. Otherwise, the **variable** is known as a free **variable**. In order to determine which **variables** are **basic** and which are free, it is necessary to row reduce the augmented matrix to echelon form. For instance, consider the system of linear equations.

**linear programming problem**consists of a

**linear**function to be maximized or minimized subject to certain constraints in the form of

**linear**equations or inequalities. Set up the following

**linear programing problems**. Do not solve.

Moreover, what is non basic variable in simplex method?

A **variable** in the **basic** solution (value is not 0). **Nonbasic Variables**. A **variable** not in the **basic** solution (value = 0). Slack **Variable**. A **variable** added to the problem to eliminate less-than constraints.

The **basis** is **optimal** if the reduced costs are negative (for a maximization problem). The **basis** is {3,4}, so the non basic variables are x1 and x2. so if x1 enters the **basis**, the objective function will increase by 155/32 for every unit of x1: the **basis** {3,4} is not **optimal**.