Extension room

Adjoining the bedroom of my house is an extension room which has a flat roof (does not have roof tiles). The house (including the bedroom) is standard BV with roof tiles. Currently there is no heating and cooling in both the rooms and I'm considering to put one, mainly the extension room is important as its walls are very thin (weatherboard) and roof is flat.

The dimensions of the extension room are 3.2mx6m and the bedroom are 3mx3.8m. I have attached the layout diagram as well with this thread. Can you please suggest some cheap temperature maintenance options around $1K including installation.


Personally I am thinking of reverse-cycle, where do you think I should place the unit for it to effective in cooling both rooms. Placeholder 1, 2 or 3?
 

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    layout.png
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Place 2 or 3 would seem to be able to "direct" the air through the door into the second room.

I think 3 is best as it is in the middle of the larger room but would still push some air through the door to the other room.
 
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