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 problem involves minimizing an objective function subject to several constraints.

The objective function is: Minimize $7x_0 + 3x_1$, where $x_0$ represents the amount of grams of protein and $x_1$ represents the amount of milligrams of vitamin D.

The constraints are as follows:
- Kidney support index for grams of protein: $15x_0$
- Cardiovascular support index for grams of protein: $5x_0$
- Kidney support index for milligrams of vitamin D: $14x_1$
- Cardiovascular support index for milligrams of vitamin D: $25x_1$
- Total combined kidney support index $\geq 33$: $15x_0 + 14x_1 \geq 33$
- Total combined cardiovascular support index $\geq 78$: $5x_0 + 25x_1 \geq 78$
- Additional constraint: $9x_0 - 6x_1 \geq 0$
- Upper bound for total kidney support index: $15x_0 + 14x_1 \leq 75$
- Upper bound for total cardiovascular support index: $5x_0 + 25x_1 \leq 189$
- $x_0$ must be an integer (no fractional grams of protein)
- $x_1$ can be any non-negative real number (milligrams of vitamin D)

Given the description, we'll implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="grams_of_protein")  # Integer variable for grams of protein
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_D")  # Continuous variable for milligrams of vitamin D

# Objective function: Minimize 7*x0 + 3*x1
m.setObjective(7*x0 + 3*x1, GRB.MINIMIZE)

# Constraints
m.addConstr(15*x0 + 14*x1 >= 33, name="kidney_support_index_min")  # Total kidney support index minimum
m.addConstr(5*x0 + 25*x1 >= 78, name="cardiovascular_support_index_min")  # Total cardiovascular support index minimum
m.addConstr(9*x0 - 6*x1 >= 0, name="additional_constraint")  # Additional constraint
m.addConstr(15*x0 + 14*x1 <= 75, name="kidney_support_index_max")  # Total kidney support index maximum
m.addConstr(5*x0 + 25*x1 <= 189, name="cardiovascular_support_index_max")  # Total cardiovascular support index maximum

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Grams of Protein: {x0.x}")
    print(f"Milligrams of Vitamin D: {x1.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```