On one nonlinear planning problem

The paper is concerned with maximization of the minimal percentage of planning targeth to be by all means achieved by process whose mathematical model is described by a system of linear inequalities with the right-hand side vector (planning tasks) belonging to a convex polyhedral set of a special form. A very simple computer realizable method for determination of all extreme points of the polyhedral set necessary for reducing the initial nonlinear planning problem to that of linear programming is suggested and the possibility of application of unidmensional optimization methods for approximate solution of the planning problem is discussed.