**Examples**
**1. ** The following is a standard maximization problem:

#[Maximize][Maximizar]# \t $p = 2x - 3y + z$ \t
\\ #[subject to][sujeto a]# \t $3y + z \leq 0$
\\ \t $2x + y - z \leq 10$ \t
\\ \t $x \geq 0, y \geq 0$.

**2. ** The following LP problem is not standard as presented, but can be rewritten a standard maximization problem:

#[Maximize][Maximizar]# \t $p = 3x-3y-8z$
\\ #[subject to][sujeto a]# \t $x-z \geq -5$
\\ \t $3y+5z \geq 0$
\\ \t $x \geq 0, y \geq 0, z \geq 0$.

We can reverse the inequality in the first and second constraint by multiplying both sides by $-1$ to obtain the following standard maximization problem:

#[Maximize][Maximizar]# \t $p = 3x-3y-8z$
\\ #[subject to][sujeto a]# \t $-x + z \leq 5$
\\ \t $-3y - 5z \leq 0$
\\ \t $x \geq 0, y \geq 0, z \geq 0$.