## Task 1 - 050911

A turner needs half an hour to manufacture a certain part. Since several identical parts need to be produced, he is considering building a fixture that would allow each such part to be manufactured in 20 minutes. The construction of this fixture would take 4 hours.

How many parts at least need to be produced for the construction of the fixture to result in time savings?
For the construction without the device, 30 minutes are required for $x$ workpieces. For the construction with the device, 20 minutes plus the 240 minutes required to build the device.

From which number of workpieces does the construction of the device become worthwhile?

$$
30 x > 20 x + 240 \rightarrow x > 24
$$

If more than 24 workpieces are produced, the prior construction of the device results in time savings.