## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of vitamin B9', 'grams of protein', 'grams of fat'], which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_0$ : milligrams of vitamin B9
- $x_1$ : grams of protein
- $x_2$ : grams of fat

## 3: Define the objective function in symbolic notation
The objective function to maximize is $9x_0 + 7x_1 + 3x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $10x_0 \leq 99$
- $5x_0 \leq 175$
- $11x_1 \leq 99$
- $x_1 \leq 175$
- $5x_2 \leq 99$
- $5x_2 \leq 175$
- $11x_1 + 5x_2 \geq 15$
- $11x_1 + 5x_2 \leq 36$
- $10x_0 + 11x_1 \leq 80$
- $10x_0 + 5x_2 \leq 43$
- $10x_0 + 11x_1 + 5x_2 \leq 43$
- $5x_0 + 5x_2 \leq 155$
- $5x_0 + x_1 + 5x_2 \leq 96$
- $x_0$ can be fractional, $x_1$ can be fractional, $x_2$ can be fractional.

## 5: Correct and Simplify Constraints
Correcting and simplifying the constraints based on the problem description:
- The muscle growth index constraints for each variable: $10x_0 \leq 99$, $11x_1 \leq 99$, $5x_2 \leq 99$.
- The immune support index constraints for each variable: $5x_0 \leq 175$, $x_1 \leq 175$, $5x_2 \leq 175$.
- Combined muscle growth index constraints: $11x_1 + 5x_2 \geq 15$, $11x_1 + 5x_2 \leq 36$, $10x_0 + 11x_1 \leq 80$, $10x_0 + 5x_2 \leq 43$, $10x_0 + 11x_1 + 5x_2 \leq 43$.
- Combined immune support index constraints: $5x_0 + 5x_2 \leq 155$, $5x_0 + x_1 + 5x_2 \leq 96$.

## 6: Create the symbolic representation dictionary
```json
{
    'sym_variables': [('x0', 'milligrams of vitamin B9'), ('x1', 'grams of protein'), ('x2', 'grams of fat')],
    'objective_function': '9*x0 + 7*x1 + 3*x2',
    'constraints': [
        '10*x0 <= 99',
        '5*x0 <= 175',
        '11*x1 <= 99',
        'x1 <= 175',
        '5*x2 <= 99',
        '5*x2 <= 175',
        '15 <= 11*x1 + 5*x2',
        '11*x1 + 5*x2 <= 36',
        '10*x0 + 11*x1 <= 80',
        '10*x0 + 5*x2 <= 43',
        '10*x0 + 11*x1 + 5*x2 <= 43',
        '5*x0 + 5*x2 <= 155',
        '5*x0 + x1 + 5*x2 <= 96'
    ]
}
```

## 7: Implement the optimization problem using Gurobi
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="milligrams_of_vitamin_B9", lb=0)
    x1 = model.addVar(name="grams_of_protein", lb=0)
    x2 = model.addVar(name="grams_of_fat", lb=0)

    # Define objective function
    model.setObjective(9 * x0 + 7 * x1 + 3 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(10 * x0 <= 99)
    model.addConstr(5 * x0 <= 175)
    model.addConstr(11 * x1 <= 99)
    model.addConstr(x1 <= 175)
    model.addConstr(5 * x2 <= 99)
    model.addConstr(5 * x2 <= 175)
    model.addConstr(11 * x1 + 5 * x2 >= 15)
    model.addConstr(11 * x1 + 5 * x2 <= 36)
    model.addConstr(10 * x0 + 11 * x1 <= 80)
    model.addConstr(10 * x0 + 5 * x2 <= 43)
    model.addConstr(10 * x0 + 11 * x1 + 5 * x2 <= 43)
    model.addConstr(5 * x0 + 5 * x2 <= 155)
    model.addConstr(5 * x0 + x1 + 5 * x2 <= 96)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin B9: {x0.varValue}")
        print(f"Grams of protein: {x1.varValue}")
        print(f"Grams of fat: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```