To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining the variables, the objective function, and the constraints using algebraic terms.

Let's denote:
- \(x_1\) as the amount of grams of protein,
- \(x_2\) as the amount of milligrams of vitamin K,
- \(x_3\) as the quantity of grams of carbohydrates.

The objective function to maximize is given by: \(4x_1 + 8x_2 + 9x_3\).

The constraints are:
1. The kidney support index for each component is given but not directly used in constraints; instead, we have combined indices.
2. The total combined kidney support index from grams of protein plus grams of carbohydrates should be greater than or equal to 51: \(11.41x_1 + 8.05x_3 \geq 51\).
3. The total combined kidney support index from milligrams of vitamin K and grams of carbohydrates must be equal to or less than 369: \(2.81x_2 + 8.05x_3 \leq 369\).
4. The total combined kidney support index from all components has to be at a maximum of 369: \(11.41x_1 + 2.81x_2 + 8.05x_3 \leq 369\).

All variables (\(x_1, x_2, x_3\)) can take non-whole number values.

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'grams of protein'), ('x2', 'milligrams of vitamin K'), ('x3', 'grams of carbohydrates')],
    'objective_function': '4*x1 + 8*x2 + 9*x3',
    'constraints': [
        '11.41*x1 + 8.05*x3 >= 51',
        '2.81*x2 + 8.05*x3 <= 369',
        '11.41*x1 + 2.81*x2 + 8.05*x3 <= 369'
    ]
}
```

Now, let's write the Gurobi code to solve this optimization problem:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="grams_of_protein")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_K")
x3 = m.addVar(vtype=GRB.CONTINUOUS, name="grams_of_carbohydrates")

# Define the objective function
m.setObjective(4*x1 + 8*x2 + 9*x3, GRB.MAXIMIZE)

# Add constraints
m.addConstr(11.41*x1 + 8.05*x3 >= 51, "kidney_support_index_protein_carbs")
m.addConstr(2.81*x2 + 8.05*x3 <= 369, "kidney_support_index_vitaminK_carbs")
m.addConstr(11.41*x1 + 2.81*x2 + 8.05*x3 <= 369, "total_kidney_support_index")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Grams of Protein: {x1.x}")
    print(f"Milligrams of Vitamin K: {x2.x}")
    print(f"Grams of Carbohydrates: {x3.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```