The oxygen supplies affect the outcome of the narrative in the way that the men have enough oxygen in their bottles so they are able to complete their climb to the summit of Mt. Everest.
Explanation:
In the story "The Final Assault," by Edmund Hillary, two man climb Mount Everest and as it has always been one of the most challenging mountains for any climber, even to professional ones, then to be assure their possibility to get to the top to the mount, the use of oxygen was fundamental to handle the latitude change.