Acoustic ukulele with a magnetic pickup...?

So, I've just been thinking and I've seen guitars that are acoustic and have magnetic pickups right? So could you do that to a uke assuming the uke had steel strings? if not why?
also if you could you could also put some volume controls on the uke itself right? i know some electric ukes have this but theirs seem to be guitar ones and that kinda looks ridiculously big on a uke. so it woudn't be that hard to custom order a smaller volume control.

and if this were all possible, around how much would it cost ?

Check out Jupiter creek instruments. They've got what you're thinking about with guitar pickups and steel strings.

http://www.jupitercreekmusic.com/

And yes, you can put volume controls on the uke. I think Kala does a good job integrating their shadow electronics, which are pretty small and still let you control volume and tone, on the side of the uke. If you go upmarket, brands like Fishman and LR Baggs also have controls that look great, and are hidden on the inside of the soundhole, so they're barely noticible at all. You'd be looking at about $250 after installation for one of the expensive pickups.

Risa has a killer electric uke with steel strings. They're not cheap, but the quality is comparable to an electric guitar at that price.