There are way too many variables to approach your situation this way since everything you mention is dependent on other factors you don't know. If you don't know what types plants then you can't figure how much space you need. Without knowing how much space, or plants, it's difficult to pick a system. Without plants and space then lighting choices can't be made correctly. Nutrient usage depends on the types of plants. And without any of that costs are impossible to figure out. You need a starting point. Something definitive to build a plan from. Plants? Budget? Space? System? I would think that if you're trying to feed 20 vegans for a year that they would know what they want to eat. Start there. Check yield and factor how many plants per person staggering plantings. You can then figure out how much space you'll need and depending on what types of plants you can select the best system and lights. Anyway, that's my 2 cents.