The Island:    How you got on the island?  Not important.  
Surrounded on all sides by salt water filled with plenty of fish.  There isn't any land for MILES out in either direction and it's a place on the map that no sane captain would ever bring his ship.  Ergo, no rescue.  Ever.  There are some wild animals on the island, but none that will attack you unprovoked.  The island has a forest with trees abound, some of which carrying edible fruit.  There are no caves on the island though.  The weather is cool, but in the winter can get harsh, with lows of 5 degrees at the most extreme.  

The Umbrella: Standard black umbrella, made with a fiberglass shaft,  nylon canopy (hand sewn), and the metal parts made from aluminum.  

The Plastic Wrap: A 50 foot roll.  Follows the basic principals of plastic wrap (will stick to itself, stretchable, etc.)  Does not come in a box.  

If you have any more questions about the Island, Umbrella, or Plastic Wrap, just ask. 

I voted for Plastic wrap, simply because I could stretch it between two tree limbs for shelter from the rain. That's the only use I can think of for now. An umbrella could shield me from the sun, but so can shade.
I'm pretty comfortable with that choice.