How to say "increase the food price" in Chinese?
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.