## Step 1: Define the symbolic representation of the variables
The variables are 'milligrams of vitamin D' and 'grams of protein', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The pairs of variables in symbolic notation are: 
- $x_1$ for 'milligrams of vitamin D'
- $x_2$ for 'grams of protein'

## 3: Define the objective function in symbolic notation
The objective function to minimize is $8.27x_1 + 9.25x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $2.3x_1 + 0.28x_2 \geq 22$
- $0.95x_1 + 1.94x_2 \geq 15$
- $2.92x_1 + 0.58x_2 \geq 12$
- $-8x_1 + 10x_2 \geq 0$
- $2.3x_1 + 0.28x_2 \leq 55$
- $0.95x_1 + 1.94x_2 \leq 60$
- $2.92x_1 + 0.58x_2 \leq 44$
- $x_1$ is a continuous variable
- $x_2$ is an integer variable

## 5: Provide the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'milligrams of vitamin D'), ('x2', 'grams of protein')],
'objective_function': '8.27*x1 + 9.25*x2',
'constraints': [
    '2.3*x1 + 0.28*x2 >= 22',
    '0.95*x1 + 1.94*x2 >= 15',
    '2.92*x1 + 0.58*x2 >= 12',
    '-8*x1 + 10*x2 >= 0',
    '2.3*x1 + 0.28*x2 <= 55',
    '0.95*x1 + 1.94*x2 <= 60',
    '2.92*x1 + 0.58*x2 <= 44'
]
}
```

## Step 6: Write the Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="milligrams_of_vitamin_D", lb=0, ub=None)
    x2 = model.addVar(name="grams_of_protein", lb=0, integer=True)

    # Define the objective function
    model.setObjective(8.27 * x1 + 9.25 * x2, gurobi.GRB.MINIMIZE)

    # Define the constraints
    model.addConstr(2.3 * x1 + 0.28 * x2 >= 22, name="muscle_growth_index_constraint")
    model.addConstr(0.95 * x1 + 1.94 * x2 >= 15, name="energy_stability_index_constraint")
    model.addConstr(2.92 * x1 + 0.58 * x2 >= 12, name="immune_support_index_constraint")
    model.addConstr(-8 * x1 + 10 * x2 >= 0, name="protein_constraint")
    model.addConstr(2.3 * x1 + 0.28 * x2 <= 55, name="muscle_growth_index_upper_bound")
    model.addConstr(0.95 * x1 + 1.94 * x2 <= 60, name="energy_stability_index_upper_bound")
    model.addConstr(2.92 * x1 + 0.58 * x2 <= 44, name="immune_support_index_upper_bound")

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```