Question: The programs work on monitors day in and day out for near untraceable period to time. What is the best position to keep the monitor?

Answer: 
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Since people are not the same (and in many companies monitors are not the same), there is no one best position.

Some people are tall, some are short. Some people see close objects well, others don't. Some people have small monitors, some have large monitors, some have more than one.

Some monitors are attached to laptops, some are independent, some are touch-screens.

The best thing to do is to allow individuals to adjust their monitor(s) (and all other office equipment) to best suit their individual needs and preferences.

You can send around the government/OSHA recommendations as a starting point, but they are just recommendations. Use what works for individuals.
I consider it obvious that human body is made for movement and human vision for relatively long-distance seeing. Thus, I infer that:

**a)** the best position for a monitor is one which is changing over periods of time. 

In this respect (at least) a laptop is ergonomic because it allows you to change its position easily. E.g. you could work one hour sitting, then one hour standing and so on. 

Another, less flexible option is to use a "monitor arm". The arm does not allow for frequent change of the position of the screen indeed, but it allows you to try different positions of the monitor until you feel comfortable. In the same manner it lets people of different heights place the monitor in the best position for themselves.

**b)** a big screen, with bigger scale of displayed content, viewed at a longer distance is better than the opposite - a small screen, tiny scale and short distance. 

(More about about bigger scale here: <https://superuser.com/questions/698121/bigger-picture-on-a-computer-display>).

Ideally the best screen would be a pocket projector with a perfectly stable image and very high brightness. The problem is that projectors are not bright enough to be usable in a sunny day.