To make more money, of course. Increasing your sales from 12% of the market to 20% of the market by offering a burger (or whatever) for $4 of pure profit instead of competitor's $6 doesn't stop the gravy train.
So, what is on one hand necessary and inelastic can also be a luxury.
Even things called 'staples' are flexible, you won't die of malnutrition if you don't eat eggs.
Which is exactly my point: either a rival corporation would be able to get market share via undercutting, or price increases are not actually that sensitive to consumer to begin with.