What was the conflict of The Cold Equations?

The conflict of Tom Godwin's short story "The Cold Equations" is that because of a mistake, Marilyn has to die, and Barton has to be the one to send her to her death.
Set in a more scientifically advanced future, Barton is piloting an Emergency Dispatch Ship carrying much-needed medicine to a colony of people that live on another planet called Woden. He discovers that a young woman named Marilyn, naive to the consequences of her actions, snuck onto the ship before takeoff, hoping that she would be able to get to see her older brother Gerry, who is currently working on Woden.
What Marilyn does not know before deciding to stow away on this ship is that it only holds enough fuel to reach its destination with one person inside. If she remains on the ship long enough, it will run out of fuel before it reaches Woden. That would mean not only the death of herself and Barton, but also the people on Woden waiting for the serum that the ship is carrying.
By law, in order to save fuel and save lives, Marilyn must be jettisoned out of the ship and into space, meaning she will die. Barton talks with his Commander to see if there's anything he can do to save her, but its no use. Marilyn goes through a lot of emotions, as would be expected, but she eventually understands that her fate cannot be changed. At the end of the story Marilyn steps into the airlock and says "I'm ready," and Barton has to pull the lever that releases her into space. The last line of the story shows us that Barton will not be getting over the guilt of this death any time soon:

It seemed, almost, that she still sat, small and bewildered and frightened, on the metal box beside him, her words echoing hauntingly clear in the void she had left behind her: I didn’t do anything to die for...I didn’t do anything...