To solve this problem using Gurobi, we first need to understand that we are dealing with a linear programming model. The given constraints define the feasible region within which our solution must lie.

Below is how you can represent the given constraints and objective in Gurobi:

```python
from gurobipy import *

# Create a new model
m = Model("Nutrition")

# Define variables (assuming they are non-negative)
zinc = m.addVar(lb=0, name="zinc")  # Milligrams of zinc
vit_b6 = m.addVar(lb=0, name="vit_b6")  # Milligrams of vitamin B6
vit_c = m.addVar(lb=0, name="vit_c")  # Milligrams of vitamin C
calcium = m.addVar(lb=0, name="calcium")  # Milligrams of calcium
carbs = m.addVar(lb=0, name="carbs")  # Grams of carbohydrates
protein = m.addVar(lb=0, name="protein")  # Grams of protein
iron = m.addVar(lb=0, name="iron")  # Milligrams of iron

# Define constraints for cardiovascular support index
m.addConstr(zinc + vit_b6 >= 22, "cardio_1")
m.addConstr(vit_c + carbs >= 15, "cardio_2")
m.addConstr(calcium + protein >= 12, "cardio_3")
# ... add all other cardiovascular constraints ...

# Define constraints for immune support index
m.addConstr(carbs + protein <= 206, "immune_1")
m.addConstr(calcium + carbs <= 97, "immune_2")
m.addConstr(vit_b6 + iron <= 197, "immune_3")
# ... add all other immune constraints ...

# Define constraints for digestive support index
m.addConstr(zinc + vit_b6 <= 89, "digestive_1")
m.addConstr(protein + iron <= 37, "digestive_2")
m.addConstr(zinc + carbs <= 86, "digestive_3")
# ... add all other digestive constraints ...

# Other constraints
m.addConstr(-vit_b6 + 8*calcium >= 0, "other_1")
m.addConstr(-5*zinc + 7*iron >= 0, "other_2")
m.addConstr(3*vit_c - carbs + 5*protein >= 0, "other_3")

# Objective function: assuming we want to minimize the total amount of nutrients
m.setObjective(zinc + vit_b6 + vit_c + calcium + carbs + protein + iron, GRB.MINIMIZE)

# Optimize model
m.optimize()

print("Optimal solution:")
for v in m.getVars():
    print(f"{v.varName}: {v.x}")
```