Arduino vs standalone microcontroller programming
You could use an AVR micro-controller in your product to run the code you develop on an Arduino development board.  

The Arduino is a good development and prototyping platform because it comes with a lot of hardware facilities ready to use, but that's what makes it too expensive for a product.  You can use the same, or a similar, kind of micro-controller chip in your product without the whole Arduino board around it.

This page from the Arduino website describes how to bread-board a bare AVR controller chip and crystal, and load your Arduino program into it.