Smoke detector placement in basement with beams exposed

Hi,

I have an unfinished basement in my rental. It has exposed floor joists and exposed underside of hardwood flooring of the first floor apartment. My question is: where is the best placement for the smoke detector to work properly? I figure there's 3 options:

1. On the underside of the hardwood flooring from the first floor (the highest point in the room)? 

2. On the fat edge/face of the floor joist?

3. On the skinny edge of the floor joist (the area closest to the floor)?