# Integer Programs

Learn to solve problems involving integer numbers.

## We'll cover the following

The special methods weāve learned so far to solve linear problems work for continuous problems, in which the variables can take any real value. However, there are some problems in which variables should be integers.

## Integer problems

For example, when we want to know the number of workers needed to accomplish a task or the number of soda cans a business owner should buy for their store, the solution canāt be a fraction. It should be an integer number.

Linear problems that are restricted to integer solutions are commonly called **integer problems**, and the field that studies the solution to those problems is **integer programming**. Formally, these problems are defined as linear problems with an additional constraint.

$\min_{\mathbf{x}} \mathbf{c}\mathbf{x}^\top\\ s.t.: P\mathbf{x}^\top \leq \mathbf{p}\\ Q\mathbf{x}^\top = \mathbf{q}\\ \mathbf{x} \in \mathbb{Z}^n$

Here, $\mathbf{x}$ is a vector with $n$ dimensions and the third constraint tells us that all of these dimensions have integer values.

Get hands-on with 1200+ tech skills courses.