## Step 1: Define the symbolic representation of the variables
The variables are 'ravioli' and 'cherry pies', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $3.16 \times \text{ravioli} + 7.63 \times \text{cherry pies}$, which in symbolic notation is $3.16x_1 + 7.63x_2$.

## 3: Define the constraints in symbolic notation
The constraints given are:
1. $17x_1 + 8x_2 \geq 20$ (at least 20 grams of carbohydrates),
2. $9x_1 + 2x_2 \geq 22$ (minimum umami index of 22),
3. $2x_1 - 2x_2 \geq 0$ (or $x_1 \geq x_2$),
4. $17x_1 + 8x_2 \leq 39$ (at most 39 grams of carbohydrates),
5. $9x_1 + 2x_2 \leq 37$ (total umami index at most 37).

## 4: Create a symbolic representation of the problem
The symbolic representation is:
- Variables: $(x_1, \text{ravioli}), (x_2, \text{cherry pies})$
- Objective function: $3.16x_1 + 7.63x_2$
- Constraints:
  1. $17x_1 + 8x_2 \geq 20$
  2. $9x_1 + 2x_2 \geq 22$
  3. $2x_1 - 2x_2 \geq 0$
  4. $17x_1 + 8x_2 \leq 39$
  5. $9x_1 + 2x_2 \leq 37$

## 5: Implement the problem in Gurobi
```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="ravioli", lb=0)  # ravioli
x2 = model.addVar(name="cherry_pies", lb=0)  # cherry pies

# Objective function: maximize 3.16 * ravioli + 7.63 * cherry_pies
model.setObjective(3.16 * x1 + 7.63 * x2, gurobi.GRB.MAXIMIZE)

# Constraints
model.addConstr(17 * x1 + 8 * x2 >= 20, name="carbohydrates_min")
model.addConstr(9 * x1 + 2 * x2 >= 22, name="umami_min")
model.addConstr(2 * x1 - 2 * x2 >= 0, name="ravioli_vs_cherry")
model.addConstr(17 * x1 + 8 * x2 <= 39, name="carbohydrates_max")
model.addConstr(9 * x1 + 2 * x2 <= 37, name="umami_max")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Ravioli: {x1.varValue}")
    print(f"Cherry pies: {x2.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("No optimal solution found.")
```

## 6: Provide the symbolic representation in the required format
```json
{
    'sym_variables': [('x1', 'ravioli'), ('x2', 'cherry pies')],
    'objective_function': '3.16x1 + 7.63x2',
    'constraints': [
        '17x1 + 8x2 >= 20',
        '9x1 + 2x2 >= 22',
        '2x1 - 2x2 >= 0',
        '17x1 + 8x2 <= 39',
        '9x1 + 2x2 <= 37'
    ]
}
```

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="ravioli", lb=0)  # ravioli
x2 = model.addVar(name="cherry_pies", lb=0)  # cherry pies

# Objective function: maximize 3.16 * ravioli + 7.63 * cherry_pies
model.setObjective(3.16 * x1 + 7.63 * x2, gurobi.GRB.MAXIMIZE)

# Constraints
model.addConstr(17 * x1 + 8 * x2 >= 20, name="carbohydrates_min")
model.addConstr(9 * x1 + 2 * x2 >= 22, name="umami_min")
model.addConstr(2 * x1 - 2 * x2 >= 0, name="ravioli_vs_cherry")
model.addConstr(17 * x1 + 8 * x2 <= 39, name="carbohydrates_max")
model.addConstr(9 * x1 + 2 * x2 <= 37, name="umami_max")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Ravioli: {x1.varValue}")
    print(f"Cherry pies: {x2.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("No optimal solution found.")
```