## Problem Description and Formulation

The problem requires minimizing an objective function subject to several constraints. The variables are 'bowls of instant ramen' (let's denote it as \(x_0\)) and 'hot dogs' (denoted as \(x_1\)). The objective function to minimize is \(6.45x_0x_1 + 2.48x_1\).

The constraints are as follows:
1. The tastiness rating of 'bowls of instant ramen' is 5, and for 'hot dogs' is 6.
2. The total tastiness rating must be at least 61: \(5x_0 + 6x_1 \geq 61\).
3. The constraint \(-6x_0 + 7x_1 \geq 0\).
4. The total combined tastiness rating squared must be at most 122: \((5x_0)^2 + (6x_1)^2 \leq 122\).
5. \(x_0\) can be any real number (no restriction on integrality).
6. \(x_1\) must be an integer.

## Gurobi Code Formulation

Given the problem description, we can formulate the Gurobi code as follows:

```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="bowls_of_instant_ramen")
    x1 = model.addVar(lb=0, ub=gurobi.GRB.INFINITY, name="hot_dogs", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(6.45 * x0 * x1 + 2.48 * x1, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(5 * x0 + 6 * x1 >= 61, name="tastiness_rating_min")
    model.addConstr(-6 * x0 + 7 * x1 >= 0, name="linear_constraint")
    model.addConstr(5 * x0 >= 0) # Not required but added for clarity on x0's domain
    model.addConstr(25 * x0**2 + 36 * x1**2 <= 122, name="tastiness_rating_squared_max")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"bowls of instant ramen: {x0.varValue}")
        print(f"hot dogs: {x1.varValue}")
        print(f"Objective: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

solve_optimization_problem()
```

## Note
The above formulation directly translates the problem description into Gurobi code. Note that for the constraint involving the squared terms, we directly use `x0**2` and `x1**2` as Gurobi supports nonlinear constraints to some extent but with limitations, especially with integer variables involved. However, for fully nonlinear problems or specific requirements, consider using Gurobi's Python API advanced features or consult the Gurobi documentation for handling nonlinear constraints and integer variables effectively. 

In a practical scenario, ensure you handle exceptions and model statuses appropriately for a robust application. 

This code provides a straightforward implementation based on the given problem and should be adjusted according to specific requirements or further constraints not mentioned.