To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

### Symbolic Representation

Let's define:
- $x_1$ as the number of bowls of instant ramen,
- $x_2$ as the number of hot dogs.

The objective function to minimize is: $6.45x_1x_2 + 2.48x_2$

The constraints are:
1. Tastiness rating of bowls of instant ramen: $5x_1$
2. Tastiness rating of hot dogs: $6x_2$
3. Total combined tastiness rating must be at least 61: $5x_1 + 6x_2 \geq 61$
4. The same as constraint 3, emphasizing it's a minimum requirement.
5. Constraint involving bowls and hot dogs: $-6x_1 + 7x_2 \geq 0$
6. Total combined squared tastiness rating must be at most 122: $(5x_1)^2 + (6x_2)^2 \leq 122$

Since we don't need an integer amount of bowls of instant ramen but must have a whole number of hot dogs, $x_1$ can be continuous, and $x_2$ must be an integer.

### Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'bowls of instant ramen'), ('x2', 'hot dogs')],
    'objective_function': '6.45*x1*x2 + 2.48*x2',
    'constraints': [
        '5*x1 + 6*x2 >= 61',
        '-6*x1 + 7*x2 >= 0',
        '(5*x1)**2 + (6*x2)**2 <= 122'
    ]
}
```

### Gurobi Code

To solve this optimization problem using Gurobi, we'll 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="bowls_of_instant_ramen", vtype=GRB.CONTINUOUS)
x2 = m.addVar(lb=0, name="hot_dogs", vtype=GRB.INTEGER)

# Set the objective function
m.setObjective(6.45*x1*x2 + 2.48*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*x1 + 6*x2 >= 61, name="total_tastiness")
m.addConstr(-6*x1 + 7*x2 >= 0, name="bowls_hot_dogs_constraint")
m.addConstr((5*x1)**2 + (6*x2)**2 <= 122, name="squared_tastiness")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of bowls of instant ramen: {x1.x}")
    print(f"Number of hot dogs: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```