Demand functions aren't generally straight like the illustrative graphs used in intro classes. What you end up with is easy replacement with similar goods. Being able to differentiate goods in food-service seems like a very difficult proposition without some sort of brand recognition. Because of that, if someone can purchase some food that is equal or close enough to equal at a significant (significance as defined by the consumer utility) then they will go with the cheaper option.
While raising prices seems like the simple solution to this issue, the reality is likely that they would quickly - if not immediately - price themselves out of the market.