学校餐厅的开支增加了，这样一来，餐厅就会 increase the food price.
How do I say "increase the food price" in Chinese?
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Word by word, the translation is:
increase(提高/增加 ti gao / zeng jia);
the food(食物shi wu);
的(pinyin: de, meaning the food'S price, or price OF the food. The character is added to express that the price is the food's);
price (价格jia ge)
So the whole sentence would be, 提高食物的价格
Although in short, you can simply say 涨价(zhang jia) meaning to increase price as @user-487 answered above.
I will translate it as “提高饭菜的价格”. “食品” is more general than “饭菜”, but sounds too general. If this sentence is describing cafeterias in Chinese universities, “饭菜” will suffice because it is unlikely they will provide anything other than 饭 and 菜 (e.g. soft drink and ice cream, which are usually sold elsewhere).