1. The production of ceramic items consists of 3 sequential stages: forming a ceramic item on a potter's wheel for 15 minutes, drying for 10 minutes, and firing for 30 minutes. It is required to produce 75 items. How should 13 masters be distributed between molders and firers to work on stages 1 and 3 respectively for the entire duration of the stage (drying does not require workers), to complete the work in the shortest time possible? In the answer, write the shortest time (in minutes) required to complete the entire job. Provide the answer as a number without indicating the unit. (5 points)
Solution. Molders - 4, decorators - 8. The thirteenth master can work at any stage, or not participate in the work at all. In this case, the working time is 325 minutes $\left(55+\left(\left[\frac{75}{4}\right]+1\right) \cdot 15=325\right)$. We will show that with other arrangements, the working time is longer. Suppose there are fewer than 4 molders (3, 2, or 1), then the time for molding is no less than 375 minutes. If there are fewer than 8 decorators, then the time for the third stage is no less than 330 minutes. Answer: 325