My name is Lianna and I am currently in the midst of my 4th year industrial design thesis project where I am designing an analog one-time-use 3-shot camera to be given out and used at promotional events, so it needs to be ultra cheap for high production runs. So whatever the housing is will end up being some kind of thin cardboard or other very cheap material but its insides could be recycled and reused when sent to the film developer during processing.
I'm using 35mm 800 ISO/APA film and there won't be any sensors or flash within the camera, somewhere between pinhole and lomography. However, because it is a product to be given out at events, it needs to be intuitive and as easy as a disposable camera to use.
Lianna, sorry to be devil's advocate here, but if you want something cheap as chips, would not a digital disposable camera be a better option. Analog requires film and processing and printing costs.