7.16. Ten workers need to assemble 50 items from parts. First, the parts of each item need to be painted; it takes one worker 10 minutes to do this. After painting, the parts dry for 5 minutes. Assembling an item takes one worker 20 minutes. How many workers should be assigned as painters and how many as assemblers to complete the work in the shortest time? (Two workers cannot paint or assemble the same item simultaneously.)

## 7.5. Correspondences
7.16. Answer: 3 painters and 6 assemblers (one worker is extra, i.e., you can assign 4 painters and 6 assemblers or 3 painters and 7 assemblers). It is easy to verify that 3 painters and 6 assemblers can complete the work in 195 minutes. Indeed, after 15 minutes from the start of the painters' work, 3 items are ready for assembly, and 3 assemblers will assemble them in 20 minutes. After that, 6 items will be ready for assembly, and the assemblers will never have to wait for the painters to finish painting the next item. After \(15 + 20 + 140 = 175\) minutes from the start of the work, \(3 + 7 \cdot 6 = 45\) items will be assembled. To assemble the remaining 5 items, another 20 minutes are needed (only 5 assemblers can work on this).

If there are fewer than three painters, painting will take no less than 250 minutes, and if there are fewer than six assemblers, assembly will take no less than 200 minutes.