# Linear Programming and Standard Form

In order to find the dual of a primal linear program, do I always have to convert it to the standard form first?

For example, if I have the following LP, would the dual also be a min since the LP in standard form is a maximization?

If the primal linear program is a maximization problem, then the dual linear program is a minimization problem and visa-versa.

Objective function

$$\text{max} \ 6y_1+10y_2-3y_3$$

Restrictions

1. $$8y_1-y_3 \leq 5$$

The sign $$\leq$$ due to $$x_1 \geq 0$$.

1. $$y_1+y_2+y_4=-7$$

The sign $$=$$ due to $$x_2$$ is unconstrained.

1. $$-y_1+3y_3-5y_4\leq 2$$

The sign $$\leq$$ due to $$x_3 \geq 0$$.

1. $$-3y_1+y_2+y_3-2y_4\leq 1$$

The sign $$\leq$$ due to $$x_4 \geq 0$$.

Variables

• $$y_1,y_3 \leq 0$$ because of the signs, $$\leq$$, at the first and third constraints at the primal problem.
• $$y_2 \geq 0$$ because of the sign, $$\geq$$, at the second constraint at the primal problem.
• $$y_4$$ is unconstrained because of the equalitiy sign at the fourth constraint at the primal problem.