Standard maximization problem
A linear programming (LP) problem is called a standard maximization problem if:

We are to find the maximum (not minimum) value of the objective function.
All the decision variables $x_1, x_2, ..., x_n$ are constrained to be non-negative.
All further constraints have the form $bx_1 + bx_2 + ... + bx_n \bold{\color{#b50b0b}{\leq}} c$ (and not $\geq c$), and $c$ cannot be negative.

Examples
1. The following is a standard maximization problem:

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

One for you

The following problem cannot be rewritten as a standard maximization problem. Indicate why by selecting the valid reasons for that conclusion (there could be only one or more than one).

#[Maximize][Maximizar]# \t $p = %0$ \\ #[subject to][sujeto a]# \t %1

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