  We present a multidimensional optimization problem that is formulated and
solved in the tropical mathematics setting. The problem consists of minimizing
a nonlinear objective function defined on vectors over an idempotent semifield
by means of a conjugate transposition operator, subject to constraints in the
form of linear vector inequalities. A complete direct solution to the problem
under fairly general assumptions is given in a compact vector form suitable for
both further analysis and practical implementation. We apply the result to
solve a multidimensional minimax single facility location problem with
Chebyshev distance and with inequality constraints imposed on the feasible
location area.
