## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'milligrams of vitamin E' and 'milligrams of vitamin C'. Let's denote 'milligrams of vitamin E' as $x_1$ and 'milligrams of vitamin C' as $x_2$. The objective function to minimize is $7x_1 + 5x_2$. The constraints are:
- $2x_1 \leq 97$
- $3x_1 \leq 29$
- $2x_2 \leq 97$
- $7x_2 \leq 29$
- $2x_1 + 2x_2 \geq 34$
- $3x_1 + 7x_2 \geq 11$
- $6x_1 - 4x_2 \geq 0$
- $2x_1 + 2x_2 \leq 72$
- $3x_1 + 7x_2 \leq 27$
- $x_1, x_2 \geq 0$ (Implicit, as they represent milligrams and can be fractional)

## 2: Correct and Simplify Constraints
Correcting and simplifying the constraints based on the problem statement:
- The cardiovascular support index for $x_1$ is 2, for $x_2$ is 2. So, $2x_1 + 2x_2 \geq 34$ and $2x_1 + 2x_2 \leq 72$.
- The muscle growth index for $x_1$ is 3, for $x_2$ is 7. So, $3x_1 + 7x_2 \geq 11$ and $3x_1 + 7x_2 \leq 27$.
- Other constraints are already given.

## 3: Symbolic Representation
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'milligrams of vitamin E'), ('x2', 'milligrams of vitamin C')],
'objective_function': '7*x1 + 5*x2',
'constraints': [
    '2*x1 <= 97',
    '3*x1 <= 29',
    '2*x2 <= 97',
    '7*x2 <= 29',
    '2*x1 + 2*x2 >= 34',
    '3*x1 + 7*x2 >= 11',
    '6*x1 - 4*x2 >= 0',
    '2*x1 + 2*x2 <= 72',
    '3*x1 + 7*x2 <= 27'
]
}
```

## 4: Gurobi Code
Now, let's write the Gurobi code for this problem:
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="milligrams_of_vitamin_E", lb=0)  # Vitamin E
    x2 = model.addVar(name="milligrams_of_vitamin_C", lb=0)  # Vitamin C

    # Objective function: Minimize 7*x1 + 5*x2
    model.setObjective(7 * x1 + 5 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(2 * x1 <= 97)
    model.addConstr(3 * x1 <= 29)
    model.addConstr(2 * x2 <= 97)
    model.addConstr(7 * x2 <= 29)
    model.addConstr(2 * x1 + 2 * x2 >= 34)
    model.addConstr(3 * x1 + 7 * x2 >= 11)
    model.addConstr(6 * x1 - 4 * x2 >= 0)
    model.addConstr(2 * x1 + 2 * x2 <= 72)
    model.addConstr(3 * x1 + 7 * x2 <= 27)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin E: {x1.varValue}")
        print(f"Milligrams of vitamin C: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```