## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'milligrams of iron' and 'milligrams of potassium'. Let's denote 'milligrams of iron' as $x_1$ and 'milligrams of potassium' as $x_2$. The objective function to minimize is $5x_1^2 + 4x_1x_2 + 3x_2^2 + 8x_1 + 7x_2$.

## Step 2: List the constraints
The constraints given are:
- The immune support index for milligrams of iron is 2: $2x_1 \leq 109$ is not directly given, instead, we have $r0: 2x_1 + 9x_2 \leq 109$.
- The muscle growth index for milligrams of iron is 10: $10x_1 \leq 65$.
- Milligrams of potassium have an immune support index of 9: This is part of $r0: 2x_1 + 9x_2 \leq 109$.
- Milligrams of potassium each have a muscle growth index of 3: $3x_2 \leq 65$ is not directly given, instead, we consider $r1: 10x_1 + 3x_2 \leq 65$.
- The total combined immune support index from milligrams of iron squared plus milligrams of potassium squared should be greater than or equal to 48: $x_1^2 + x_2^2 \geq 48$ is not directly given, instead, we have $r0: 2x_1 + 9x_2 \geq 0$ and another constraint $x_1 + x_2 \geq 48$ is not directly provided but $2x_1 + 9x_2 \geq 48$ and $x_1 + x_2 \geq 48$ seems to be misinterpreted. Correctly, we have $x_1^2 + x_2^2 \geq 48$ and $x_1 + x_2 \geq 48$.
- The total combined immune support index from milligrams of iron plus milligrams of potassium should be no less than 48: $x_1 + x_2 \geq 48$.
- The total combined muscle growth index from milligrams of iron plus milligrams of potassium must be at least 18: $10x_1 + 3x_2 \geq 18$.
- $-6x_1 + 5x_2 \geq 0$.
- The total combined immune support index from milligrams of iron plus milligrams of potassium should be at maximum 56: $x_1 + x_2 \leq 56$.
- The total combined muscle growth index from milligrams of iron plus milligrams of potassium should be less than or equal to 55: $10x_1 + 3x_2 \leq 55$.
- $x_1$ can be non-integer, $x_2$ must be an integer.

## 3: Correctly formulate the symbolic representation
Given variables: 
- $x_1$ for 'milligrams of iron'
- $x_2$ for 'milligrams of potassium'

Objective function: $5x_1^2 + 4x_1x_2 + 3x_2^2 + 8x_1 + 7x_2$

Constraints:
- $2x_1 + 9x_2 \leq 109$
- $10x_1 \leq 65$
- $10x_1 + 3x_2 \leq 65$
- $x_1^2 + x_2^2 \geq 48$
- $x_1 + x_2 \geq 48$
- $10x_1 + 3x_2 \geq 18$
- $-6x_1 + 5x_2 \geq 0$
- $x_1 + x_2 \leq 56$
- $10x_1 + 3x_2 \leq 55$

## 4: Provide the symbolic representation in the required format
```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': [
        '2*x1 + 9*x2 <= 109',
        '10*x1 <= 65',
        '10*x1 + 3*x2 <= 65',
        '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'
    ]
}
```

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

def optimize_problem():
    model = gurobi.Model()
    
    # Define variables
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x1")  # milligrams of iron
    x2 = model.addVar(lb=0, ub=gurobi.GRB.INFINITY, name="x2", vtype=gurobi.GRB.INTEGER)  # milligrams of potassium
    
    # Objective function
    model.setObjective(5*x1**2 + 4*x1*x2 + 3*x2**2 + 8*x1 + 7*x2, gurobi.GRB.MINIMIZE)
    
    # Constraints
    model.addConstr(2*x1 + 9*x2 <= 109)
    model.addConstr(10*x1 <= 65)
    model.addConstr(10*x1 + 3*x2 <= 65)
    model.addConstr(x1**2 + x2**2 >= 48)
    model.addConstr(x1 + x2 >= 48)
    model.addConstr(10*x1 + 3*x2 >= 18)
    model.addConstr(-6*x1 + 5*x2 >= 0)
    model.addConstr(x1 + x2 <= 56)
    model.addConstr(10*x1 + 3*x2 <= 55)
    
    # Solve the model
    model.optimize()
    
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of iron: {x1.varValue}")
        print(f"Milligrams of potassium: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    elif model.status == gurobi.GRB.Status.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

optimize_problem()
```