To solve the given optimization problem, we will use the Gurobi Python library. The problem involves minimizing an objective function subject to several constraints.

The objective function is: `7 * x0 + 5 * x1`, where `x0` represents the milligrams of vitamin E and `x1` represents the milligrams of vitamin C.

The constraints are:
- Cardiovascular support index for vitamin E: `2 * x0`
- Muscle growth index for vitamin E: `3 * x0`
- Cardiovascular support index for vitamin C: `2 * x1`
- Muscle growth index for vitamin C: `7 * x1`
- Total combined cardiovascular support index: `2 * x0 + 2 * x1 >= 34`
- Total combined muscle growth index: `3 * x0 + 7 * x1 >= 11`
- Additional constraint: `6 * x0 - 4 * x1 >= 0`
- Upper bound for total combined cardiovascular support index: `2 * x0 + 2 * x1 <= 72`
- Upper bound for total combined muscle growth index: `3 * x0 + 7 * x1 <= 27`

Given the problem statement, we can directly translate these conditions into a Gurobi model.

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_E")
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_C")

# Objective function: minimize 7*x0 + 5*x1
m.setObjective(7 * x0 + 5 * x1, GRB.MINIMIZE)

# Constraints
m.addConstr(2 * x0 + 2 * x1 >= 34, name="cardiovascular_support_index")
m.addConstr(3 * x0 + 7 * x1 >= 11, name="muscle_growth_index")
m.addConstr(6 * x0 - 4 * x1 >= 0, name="additional_constraint")
m.addConstr(2 * x0 + 2 * x1 <= 72, name="upper_bound_cardiovascular")
m.addConstr(3 * x0 + 7 * x1 <= 27, name="upper_bound_muscle_growth")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Milligrams of Vitamin E: {x0.x}")
    print(f"Milligrams of Vitamin C: {x1.x}")
else:
    print("No optimal solution found.")

```