To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables for each item (ravioli and cherry pies), formulating the objective function using these variables, and listing all constraints in terms of these variables.

Let's define:
- \(x_1\) as the quantity of ravioli,
- \(x_2\) as the quantity of cherry pies.

The objective function to maximize is given by:
\[3.16x_1 + 7.63x_2\]

Now, let's list the constraints based on the problem description:
1. The total grams of carbohydrates from ravioli and cherry pies should be at least 20 grams.
   - Since there are 17 grams of carbohydrates in each ravioli and 8 grams in each cherry pie, this constraint can be written as: \(17x_1 + 8x_2 \geq 20\)
2. The total combined umami index from ravioli and cherry pies should be at least 22.
   - Given that ravioli have a umami index of 9 each and cherry pies have an index of 2, this constraint is: \(9x_1 + 2x_2 \geq 22\)
3. The constraint \(2x_1 - 2x_2 \geq 0\) translates to "2 times the number of ravioli, minus 2 times the number of cherry pies must be at least zero."
4. At most 39 grams of carbohydrates can come from ravioli and cherry pies.
   - This constraint is represented as: \(17x_1 + 8x_2 \leq 39\)
5. The total combined umami index from ravioli plus cherry pies must be at most 37.
   - This gives us the inequality: \(9x_1 + 2x_2 \leq 37\)

Given that we can use fractional numbers of both ravioli and cherry pies, all variables are continuous.

The symbolic representation of this problem in JSON format is:
```json
{
    'sym_variables': [('x1', 'ravioli'), ('x2', 'cherry pies')],
    'objective_function': '3.16*x1 + 7.63*x2',
    'constraints': [
        '17*x1 + 8*x2 >= 20',
        '9*x1 + 2*x2 >= 22',
        '2*x1 - 2*x2 >= 0',
        '17*x1 + 8*x2 <= 39',
        '9*x1 + 2*x2 <= 37'
    ]
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="ravioli")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="cherry_pies")

# Set the objective function
m.setObjective(3.16*x1 + 7.63*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(17*x1 + 8*x2 >= 20, "carbohydrates_min")
m.addConstr(9*x1 + 2*x2 >= 22, "umami_min")
m.addConstr(2*x1 - 2*x2 >= 0, "ravioli_vs_pies")
m.addConstr(17*x1 + 8*x2 <= 39, "carbohydrates_max")
m.addConstr(9*x1 + 2*x2 <= 37, "umami_max")

# Optimize the model
m.optimize()

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