To solve the optimization problem described, 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 given information.

The variables are:
- $x_1$: The amount of green beans.
- $x_2$: The amount of bowls of cereal.

The objective function is to maximize: $6x_1 + 6x_2$.

The constraints based on the description are:
1. Healthiness rating minimum: $12x_1 + 3x_2 \geq 31$.
2. Calcium minimum: $14x_1 + 10x_2 \geq 16$.
3. Carbohydrates minimum: $10x_1 + 6x_2 \geq 13$.
4. Mixed constraint: $-2x_1 + 9x_2 \geq 0$.
5. Healthiness rating maximum: $12x_1 + 3x_2 \leq 65$.
6. Calcium maximum: $14x_1 + 10x_2 \leq 35$.
7. Carbohydrates maximum: $10x_1 + 6x_2 \leq 36$.
8. Integer constraint for green beans: $x_1$ must be an integer.

Symbolic representation:
```json
{
    'sym_variables': [('x1', 'green beans'), ('x2', 'bowls of cereal')],
    'objective_function': '6*x1 + 6*x2',
    'constraints': [
        '12*x1 + 3*x2 >= 31',
        '14*x1 + 10*x2 >= 16',
        '10*x1 + 6*x2 >= 13',
        '-2*x1 + 9*x2 >= 0',
        '12*x1 + 3*x2 <= 65',
        '14*x1 + 10*x2 <= 35',
        '10*x1 + 6*x2 <= 36'
    ]
}
```

To implement this in Gurobi, we'll use Python. The code will define the model, variables, objective function, and constraints as per the symbolic representation.

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="green_beans")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="bowls_of_cereal")

# Set the objective function
m.setObjective(6*x1 + 6*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(12*x1 + 3*x2 >= 31, "healthiness_rating_min")
m.addConstr(14*x1 + 10*x2 >= 16, "calcium_min")
m.addConstr(10*x1 + 6*x2 >= 13, "carbohydrates_min")
m.addConstr(-2*x1 + 9*x2 >= 0, "mixed_constraint")
m.addConstr(12*x1 + 3*x2 <= 65, "healthiness_rating_max")
m.addConstr(14*x1 + 10*x2 <= 35, "calcium_max")
m.addConstr(10*x1 + 6*x2 <= 36, "carbohydrates_max")

# Optimize the model
m.optimize()

# Print the results
for v in m.getVars():
    print(f"{v.varName}: {v.x}")

print("Objective:", m.objVal)
```