This contribution deals with the optimization of the amount of cooling water which cools the inner wall of the plunger in the process of manufacturing the glass vase. The system of mould, glass piece, plunger and plunger cavity is cooled from a circular tube system located inside the plunger cavity. The goal of optimization is to control the temperature distribution in the plunger during the press cycle of production in the glass industry. The state problem is given by the steady heat equation in the whole system. The cooling performance is controlled by changing the amounts of water supplied by the individual tubes. The cost functional is the squared L_r~2 norm of the difference between a prescribed constant and the temperature on the outward boundary of the plunger. Existence of the unique solution of the state problem and existence of a solution of the optimization problem are proved.
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