# Dual problem of a maximization primal problem $P$?

Suppose we have a primal problem $P$ which is stated as a maximization problem $\max c^{T} x$.

The dual problem is defined (Introduction to Linear Optimization by Dimitris Bertsimas) only for a primal minimization problem.

Then what is the dual problem of $P$ ?

Is it implicit, that the dual problem of $P$ is the dual problem of $P$ stated as the minimization problem $\min -c^T x$ ?

Surely these two primal problems are equivalent in the sense that their optimal solution $\bar x$ are equal (if it exist). However, the objective values are the same only if we ignore the sign !