There are lots of reasons why a trip to Mars is going to be an amazing challenge. Besides the risks from cosmic rays, micro-meteorites and simple insanity from being cooped up in too small a space for too long, there's the problem of fuel. The ship has to carry enough fuel to get to Mars and then get back. And the ship has to carry enough fuel -- food -- for the people on board.
If you look at the needs of a typical male, a person needs the following on a daily basis:
We can assume that the food can be supplemented with vitamins and minerals (either mixed in or as tablets), so there's no need to worry about that part of the equation. The whole problem comes down to calories, protein, fat and fiber.
If you want to be a minimalist about it, you can get your calories from white sugar, your fat from vegetable oil, your protein from protein powder and your fiber from bran. In this case, each person on the two-year journey would need:
If you formed all of those ingredients into bars or kibble, you would need about 400 kilograms, or 880 pounds, of food per person. When you buy dog food at the grocery store, a typical large bag holds 20 pounds. So you would need 44 large dog-food-sized bags to keep one person alive for two years. All of that would fit into a cube approximately 5 feet (1.5 meters) by 5 feet by 5 feet in size.
- 274 kilograms (602 pounds) of sugar
- 60 kilograms (133 pounds) of vegetable oil
- 43 kilograms (96 pounds) of protein
- 18 kilograms (40 pounds) of fiber
Most people like a little variety to their food, so all of this bulk would have to be formed into meals that at least sound interesting. That might increase the size slightly because of the packaging, but the weight of the food would be the same.
The other thing a person needs is water. On most space missions, water is a by-product of electricity production in fuel cells, so it is not a big concern. For drinking, a person would need something like 365 gallons (1,500 liters) for a two-year mission. The water would take up about as much space as the food.
Here are several interesting links: