We give an account of the primal conical internal method. While the method is primal, it uses, both in an enumerative and in an evolutive manner, the same technique of the dual method to compute the generators of a polyhedral cone, which is the intersection of a linear subspace with the positive cone. Moreover, the method allows to give, in a primal context, a formula for the value of the maximum. It also provides a complete description of the contact polytope and hence of the set of solutions.