scipy.optimize.linprog: What happens if we choose the coefficients orthogonal to the feasible set?

I am using scipy.optimize.linprog to solve a linear program. In particular, I have the constraint x_1 + ... x_n = 1, i.e. my feasible set is a subset of the n-dimensional simplex. Now, I am asking myself what happens when I choose the coefficients c of the minimization as c = (1, ..., 1). The minimization is then irrelevant, since <c, x> = 1 always.

What result does scipy.optimize.linprog give me in this situation?

I tested it, but I couldn't tell which element in the feasible set was calculated by the program. My guess it that it is a random vertex of the polytope resulting from the other inequality constraints. Can somebody confirm this?

from scipy.optimize.linprog: What happens if we choose the coefficients orthogonal to the feasible set?