If your interest is mainly culinary then you should get a culinary degree from the CIA or JW and then get a Food Science (FS) degree from a good school. This will steer you toward a Research Chef position at places like McCormick, Schwann's foods, Kerry Foods. These are places who use chefs to develop concepts and flavors but requires their chefs to understand the food manufacturing process and work with food scientists who do flavor work and scaleup formulations, the engineering group, packaging engineers, the marketing group which does market research, the sales group, etc. Of course there's a lot more than that alone. This is just a start.
Currently, there is absolutely no 4 year school which wasn't a cooking school first which offers even a semi decent culinary program. None, forget the culinary/FS degree. Go to a real cooking school for that.