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

### Symbolic Representation

Let's define:
- $x_1$ as the amount of bananas,
- $x_2$ as the number of milkshakes.

The **objective function** to maximize is given by: 
\[9.92 \cdot x_1 \cdot x_2 + 7.8 \cdot x_2^2 + 3.23 \cdot x_1 + 6.31 \cdot x_2\]

The **constraints** are:
1. $x_1 \geq 0$ (non-negativity constraint for bananas, implicitly satisfied in the context of this problem)
2. $x_2 \geq 0$ (non-negativity constraint for milkshakes)
3. $1 \cdot x_1 + 6 \cdot x_2 \leq 47$ (grams of fat constraint from 'r0')
4. $x_1^2 + x_2^2 \geq 15$ (minimum grams of fat squared from bananas and milkshakes)
5. $7 \cdot x_1^2 - 8 \cdot x_2^2 \geq 0$ (constraint on the squares of bananas and milkshakes)
6. $x_1 + 6 \cdot x_2 \leq 36$ (alternative constraint on grams of fat from bananas and milkshakes, but since it's identical in effect to constraint 3 when considering only non-negative values of $x_1$ and $x_2$, we'll focus on the distinct constraints)

### Solution in JSON Format
```json
{
    'sym_variables': [('x1', 'bananas'), ('x2', 'milkshakes')],
    'objective_function': '9.92*x1*x2 + 7.8*x2**2 + 3.23*x1 + 6.31*x2',
    'constraints': [
        'x1 + 6*x2 <= 47', 
        'x1**2 + x2**2 >= 15', 
        '7*x1**2 - 8*x2**2 >= 0', 
        'x1 + 6*x2 <= 36'
    ]
}
```

### Gurobi Code
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name="bananas", lb=0)
x2 = m.addVar(name="milkshakes", lb=0)

# Set the objective function
m.setObjective(9.92*x1*x2 + 7.8*x2**2 + 3.23*x1 + 6.31*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + 6*x2 <= 47, name="fat_constraint")
m.addConstr(x1**2 + x2**2 >= 15, name="min_fat_squared")
m.addConstr(7*x1**2 - 8*x2**2 >= 0, name="squared_constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Bananas: {x1.x}")
    print(f"Milkshakes: {x2.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```