Methods of correction (approximation) for inconsistent systems of linear algebraic equations and inequalities and improper linear programming problems have been widely used. In this paper, we consider an improper linear programming problem with an empty admissible set. It is formalized in the form of the problem of maximizing the initial criterion with the upper bound on the Frobenius norm of the correction matrix of the left-hand side of the constraints. A range of threshold values is found for which this problem has a solution, and its solution is obtained in an analytical form.