To solve the given optimization problem, 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 milligrams of iron,
- $x_2$ as the milligrams of potassium.

The objective function is given as: 
\[5(x_1)^2 + 4(x_1)(x_2) + 3(x_2)^2 + 8(x_1) + 7(x_2)\]

The constraints are:
1. $2(x_1) \geq 0$ (always true since $x_1$ is non-negative by definition)
2. $10(x_1) \geq 0$ (always true for the same reason as above)
3. $9(x_2) \geq 0$ (always true since $x_2$ is non-negative by definition)
4. $3(x_2) \geq 0$ (always true for the same reason as above)
5. $(x_1)^2 + (x_2)^2 \geq 48$
6. $x_1 + x_2 \geq 48$
7. $10(x_1) + 3(x_2) \geq 18$
8. The same as constraint 7, so we consider it only once.
9. $-6(x_1) + 5(x_2) \geq 0$
10. $x_1 + x_2 \leq 56$
11. $10(x_1) + 3(x_2) \leq 55$

The symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'milligrams of iron'), ('x2', 'milligrams of potassium')],
    'objective_function': '5*(x1)**2 + 4*x1*x2 + 3*(x2)**2 + 8*x1 + 7*x2',
    'constraints': [
        '(x1)**2 + (x2)**2 >= 48',
        'x1 + x2 >= 48',
        '10*x1 + 3*x2 >= 18',
        '-6*x1 + 5*x2 >= 0',
        'x1 + x2 <= 56',
        '10*x1 + 3*x2 <= 55'
    ]
}
```

To solve this optimization problem using Gurobi, we need to write the following Python code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, name="milligrams_of_iron")
x2 = m.addVar(vtype=GRB.INTEGER, lb=0, name="milligrams_of_potassium")

# Set the objective function
m.setObjective(5*x1**2 + 4*x1*x2 + 3*x2**2 + 8*x1 + 7*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(x1**2 + x2**2 >= 48, name="immune_support_index_combined")
m.addConstr(x1 + x2 >= 48, name="total_immune_support_index")
m.addConstr(10*x1 + 3*x2 >= 18, name="muscle_growth_index_combined")
m.addConstr(-6*x1 + 5*x2 >= 0, name="iron_potassium_ratio")
m.addConstr(x1 + x2 <= 56, name="max_total_immune_support_index")
m.addConstr(10*x1 + 3*x2 <= 55, name="max_muscle_growth_index_combined")

# Optimize model
m.optimize()

if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of iron: {x1.X}")
    print(f"Milligrams of potassium: {x2.X}")
    print(f"Objective function value: {m.ObjVal}")
else:
    print("No optimal solution found")
```