[ $\left.\begin{array}{c}\text { Work Problems } \\ \text { [ Processes and Operations }\end{array}\right]$

In a turning shop, parts are machined from steel blanks, one part from one blank. The chips left after processing three blanks can be melted down to make exactly one blank. How many parts can be made from nine blanks? From fourteen? How many blanks need to be taken to get forty parts?
From nine blanks, on the first stage, you can obtain nine parts, and from the remaining swarf, you can make three blanks, from which (on the second stage) you can make three parts, and from the remaining swarf, you can make one blank and then one part. In total, 13 parts.

With 14 blanks, it is easier to proceed as follows. Temporarily set aside two blanks and first obtain 12 parts and swarf for four blanks. By adding these four blanks to the two set aside, you will get another six parts and swarf for two blanks. Finally, make two more parts. In total, 20 parts.

If we obtained 20 parts from 14 blanks, then we can certainly obtain 40 parts from 28 blanks. Let's try to reduce this number. Take 27 blanks. First, you will get 27 parts and swarf for nine blanks. From these nine blanks, as we saw above, you can obtain 13 parts. In total, 40 parts.

26 blanks, as it is not difficult to verify, are insufficient.

## Answer

13 parts; 20 parts; 27 blanks.