## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'milligrams of vitamin C' and 'milligrams of vitamin B4'. Let's denote 'milligrams of vitamin C' as $x_1$ and 'milligrams of vitamin B4' as $x_2$. The objective function to maximize is $2.04x_1 + 8.38x_2$. The constraints are:
- $0.24x_1 + 0.73x_2 \geq 20$
- $0.03x_1 + 0.9x_2 \geq 27$
- $4x_1 - 2x_2 \geq 0$
- $0.24x_1 + 0.73x_2 \leq 36$
- $0.03x_1 + 0.9x_2 \leq 51$
- $x_1$ is an integer
- $x_2$ can be a real number

## Step 2: Convert the problem into a Gurobi-compatible format
We need to express the problem in a way that Gurobi can understand. This involves defining the variables, the objective function, and the constraints.

## 3: Define the variables and the objective function in Gurobi
In Gurobi, we define $x_1$ as an integer variable and $x_2$ as a continuous variable. The objective function is $2.04x_1 + 8.38x_2$.

## 4: Express the constraints in Gurobi
The constraints are:
- $0.24x_1 + 0.73x_2 \geq 20$
- $0.03x_1 + 0.9x_2 \geq 27$
- $4x_1 - 2x_2 \geq 0$
- $0.24x_1 + 0.73x_2 \leq 36$
- $0.03x_1 + 0.9x_2 \leq 51$

## 5: Write down the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'milligrams of vitamin C'), ('x2', 'milligrams of vitamin B4')],
'objective_function': '2.04*x1 + 8.38*x2',
'constraints': [
    '0.24*x1 + 0.73*x2 >= 20',
    '0.03*x1 + 0.9*x2 >= 27',
    '4*x1 - 2*x2 >= 0',
    '0.24*x1 + 0.73*x2 <= 36',
    '0.03*x1 + 0.9*x2 <= 51'
]
}
```

## 6: Implement the problem in Gurobi
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(vtype=gurobi.GRB.INTEGER, name="x1")  # milligrams of vitamin C
    x2 = model.addVar(vtype=gurobi.GRB.CONTINUOUS, name="x2")  # milligrams of vitamin B4

    # Define the objective function
    model.setObjective(2.04 * x1 + 8.38 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(0.24 * x1 + 0.73 * x2 >= 20, name="immune_support_index_min")
    model.addConstr(0.03 * x1 + 0.9 * x2 >= 27, name="kidney_support_index_min")
    model.addConstr(4 * x1 - 2 * x2 >= 0, name="vitamin_constraint")
    model.addConstr(0.24 * x1 + 0.73 * x2 <= 36, name="immune_support_index_max")
    model.addConstr(0.03 * x1 + 0.9 * x2 <= 51, name="kidney_support_index_max")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin C: {x1.varValue}")
        print(f"Milligrams of vitamin B4: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```