To solve the given optimization problem using Gurobi, we need to translate the natural language description into a mathematical formulation that can be implemented in Python. The objective function to minimize is:

9 * (grams of fat) + 4 * (milligrams of vitamin B2) + 2 * (milligrams of vitamin B3)

Subject to several constraints involving cardiovascular support indices and relationships between the variables.

Here's how we interpret the problem into a mathematical model:

- Let x0 be the quantity of grams of fat.
- Let x1 be the quantity of milligrams of vitamin B2.
- Let x2 be the quantity of milligrams of vitamin B3.

The objective function is: 9x0 + 4x1 + 2x2

Constraints:
1. The total combined cardiovascular support index from grams of fat plus milligrams of vitamin B3 must be at least 19: 3.84x0 + 5.67x2 ≥ 19
2. The total combined cardiovascular support index from grams of fat plus milligrams of vitamin B2 should be at least 16: 3.84x0 + 4.56x1 ≥ 16
3. The total combined cardiovascular support index from all three must be at least 16: 3.84x0 + 4.56x1 + 5.67x2 ≥ 16
4. Three times the number of milligrams of vitamin B2, plus minus two times the number of milligrams of vitamin B3 has to be greater than or equal to zero: 3x1 - 2x2 ≥ 0

Additionally, we consider the variable types:
- x0 (grams of fat) can be non-integer.
- x1 (milligrams of vitamin B2) must be an integer.
- x2 (milligrams of vitamin B3) can be non-integer.

Given these constraints and the objective function, here is how you could model this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="grams_of_fat")
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="milligrams_of_vitamin_B2")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B3")

# Objective function
m.setObjective(9*x0 + 4*x1 + 2*x2, GRB.MINIMIZE)

# Constraints
m.addConstr(3.84*x0 + 5.67*x2 >= 19, "cardiovascular_support_index_1")
m.addConstr(3.84*x0 + 4.56*x1 >= 16, "cardiovascular_support_index_2")
m.addConstr(3.84*x0 + 4.56*x1 + 5.67*x2 >= 16, "total_cardiovascular_support_index")
m.addConstr(3*x1 - 2*x2 >= 0, "vitamin_b2_and_b3_relationship")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"grams_of_fat: {x0.x}")
    print(f"milligrams_of_vitamin_B2: {x1.x}")
    print(f"milligrams_of_vitamin_B3: {x2.x}")
else:
    print("No optimal solution found")
```