The manual is designed to teach students to solve problems on the course "Variation calculus and optimization methods" (VIMO) . Solving problems in VIMO is not a simple matter that requires not only knowledge of the subject, but also a certain intuition and ingenuity . To develop these qualities, it is necessary to gain experience in solving such problems, t. e. It is easy for them to decide.... The tasks are complicated gradually, the most difficult are the tasks of optimal management, they are placed at the end of the methodological manual. It is recommended to first study the rules of the decision, and then try to decide on their own, if necessary, looking into the manual