## Step 1: Define the symbolic representation of the variables
The variables are 'knishes' and 'protein bars', which can be represented symbolically as 'x1' and 'x2' respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $1.71x_1^2 + 1.41x_1x_2 + 6.44x_2^2$.

## 3: Define the constraints in symbolic notation
The constraints are:
- $5x_1$ (milligrams of iron from knishes)
- $5x_2$ (milligrams of iron from protein bars)
- $5x_1^2 + 5x_2^2 \geq 46$ (at least 46 milligrams of iron from knishes and protein bars squared)
- $6x_1 - 3x_2 \geq 0$ (6 times the number of knishes, plus -3 times the number of protein bars should be at minimum zero)
- $5x_1^2 + 5x_2^2 \leq 52$ (at most 52 milligrams of iron from knishes squared plus protein bars squared)
- $5x_1 + 5x_2 \leq 52$ (at most 52 milligrams of iron from knishes plus protein bars)
- $x_1$ is an integer (knishes must be an integer amount)
- $x_2$ can be any real number (protein bars do not have to be a whole number)

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'knishes'), ('x2', 'protein bars')],
'objective_function': '1.71*x1^2 + 1.41*x1*x2 + 6.44*x2^2',
'constraints': [
    '5*x1^2 + 5*x2^2 >= 46',
    '6*x1 - 3*x2 >= 0',
    '5*x1^2 + 5*x2^2 <= 52',
    '5*x1 + 5*x2 <= 52',
    'x1 is an integer'
]
}
```

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

# Define the model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(vtype=gurobi.GRB.INTEGER, name="knishes")
x2 = model.addVar(vtype=gurobi.GRB.CONTINUOUS, name="protein_bars")

# Objective function
model.setObjective(1.71*x1**2 + 1.41*x1*x2 + 6.44*x2**2, gurobi.GRB.MAXIMIZE)

# Constraints
model.addConstr(5*x1**2 + 5*x2**2 >= 46, name="iron_from_squares")
model.addConstr(6*x1 - 3*x2 >= 0, name="knishes_vs_protein_bars")
model.addConstr(5*x1**2 + 5*x2**2 <= 52, name="max_iron_from_squares")
model.addConstr(5*x1 + 5*x2 <= 52, name="max_iron")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Knishes: {x1.varValue}")
    print(f"Protein Bars: {x2.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("No optimal solution found.")
```