I am a member of the AMVETS Post 312 and I could use your help.

For 175 people, assuming self serve,

corn beef, raw, 85 pounds
potatoes, 65 pounds (or you can do 50 potato and 15 rutabaga)
carrots, 18 pounds
cabbage, 45 pounds (remember to cook only last 20-30 minutes)
onions, 8 pounds
simmering liquid, about 7 gallons; you could use broth, but the meat is already so salty, I suggest water and pickling spice blend. Here is about the right amount for liquid;
Pickling spices:

1 Tbsp whole allspice berries
1 Tbsp whole mustard seeds (brown or yellow)
1 Tbsp coriander seeds
1 Tbsp red pepper flakes
1 Tbsp whole cloves
1 Tbsp whole black peppercorns
9 whole cardamom pods
6 large bay leaves, crumbled
2 teaspoons ground ginger
1/2 stick cinnamon
garlic to taste, up to 4 whole heads

You can also use straight pickling spice, 3 tablespoons per gallon, with garlic and cardamon added.

I cook the corned beef ahead ( usually bake it), take out, let cool, chill, up to 2 days before; cook the vegetables day of in the saved chilled broth, adding the cabbage only the last 20-30 minutes; meanwhile, slice and reheat the sliced beef tightly covered in the oven with some of the broth, about 30-45 minutes at preheated 350.