The cosmetic surgery machine in the game actually looks like that. I think it's supposed to be some kind of tray but I prefer to interpret it as the Happy Face-er 2000 skin resurfacing module. Dr.Chakwas' first name is never revealed so I am going to assume it is "Cleopatra". Edit the mass effect wiki accordingly.

Some notes:

• 32,000 ounces in one short ton
  
• 50,000 tons = 1.6 billion ounces
  
• In 2008 the price of platinum ranged from $774 to $2,252 per ounce
  
• Thats $1.2 to $3.6 trillion for 50,000 tons
  
• 50,000 tons of platinum could form a solid cube approximately 12.84 meters on a side
  
• In 2006 only 239 tons of platinum were sold
  
  

Transcript:
Mass Effect Comic 'Medical Results'

Panel 1
Dr.Chakwas: Stop squirming, I'm almost done.
Shepard: Ow! Well it hurts!
Dr.Chakwas: Well if you'd stop squirming it wouldn't hurt so much. There. Good as new.

Panel 2
Shepard: Ah.. Thanks Doc. This machine is ah.. great and all but it doesn't look like it weighs 50,000 tons. Where did all that platinum go?

Panel 3

[Somewhere in the desert, an enormous, solid platinum statue of Dr.Chakwas riding an elephant reads: All Hail Cleopatra Chakwas God-Queen of All Medicine]