Classic Movie?

I've been for years trying to find the title of a classic movie that I watched when I was a little boy. It tells the story of a group of people that reached a lifeboat after the ship they were in sunk. More people kept reaching the boat and it capacity didn't allow that many persons in so several of them had to be in the water, just clinging to the boat ropes. There was someone acting as a captain and determined that some people had to be let go off the boat in order to save the majority of the survivors, because otherwise they would all die. So the old and sick were left behind in the open sea as the boat went on its course. The next day they were rescued and the captain was accused of murder by the survivors who never agreed on what he did to those people he left behind. Does any one know the title of this movie?

LifeBoat is not the one, I bought it thinking it was the one I was looking for but is a totally different movie.

There is the 1957 movie "Seven Waves Away" (also used the title "Abandon Ship") starring Tyrone Power http://www.imdb.com/title/tt0050091/

and a remake called "The Last Survivors" starring Martin Sheen http://www.imdb.com/title/tt0073269/

Both sound like the film you are describing

"Lifeboat" made in 1944 by Alfred Hitchcock starring Tallulah Bankhead.