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 (corn cobs and cherry pies), formulating the objective function using these variables, and listing all constraints in terms of these variables.

### Symbolic Representation

Let's define:
- \(x_1\) as the number of corn cobs,
- \(x_2\) as the number of cherry pies.

The objective function is to maximize \(7.91x_1 + 4.62x_2\).

Constraints are as follows:
1. Fat constraint: \(20x_1 + 16x_2 \geq 56\) and \(20x_1 + 16x_2 \leq 101\)
2. Sourness index constraint: \(15x_1 + 16x_2 \geq 39\) and \(15x_1 + 16x_2 \leq 47\)
3. Calcium constraint: \(16x_1 + 15x_2 \geq 25\) and \(16x_1 + 15x_2 \leq 97\)
4. Additional linear constraint: \(-3x_1 + 9x_2 \geq 0\)

Given that \(x_1\) can be a non-integer (continuous) variable, but \(x_2\) must be an integer, we have a mixed-integer linear programming (MILP) problem.

### Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'corn cobs'), ('x2', 'cherry pies')],
    'objective_function': '7.91*x1 + 4.62*x2',
    'constraints': [
        '20*x1 + 16*x2 >= 56',
        '20*x1 + 16*x2 <= 101',
        '15*x1 + 16*x2 >= 39',
        '15*x1 + 16*x2 <= 47',
        '16*x1 + 15*x2 >= 25',
        '16*x1 + 15*x2 <= 97',
        '-3*x1 + 9*x2 >= 0'
    ]
}
```

### Gurobi Code

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

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="corn_cobs")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="cherry_pies")

# Set the objective function
m.setObjective(7.91*x1 + 4.62*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(20*x1 + 16*x2 >= 56, "fat_min")
m.addConstr(20*x1 + 16*x2 <= 101, "fat_max")
m.addConstr(15*x1 + 16*x2 >= 39, "sourness_min")
m.addConstr(15*x1 + 16*x2 <= 47, "sourness_max")
m.addConstr(16*x1 + 15*x2 >= 25, "calcium_min")
m.addConstr(16*x1 + 15*x2 <= 97, "calcium_max")
m.addConstr(-3*x1 + 9*x2 >= 0, "additional_constraint")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"corn_cobs: {x1.x}, cherry_pies: {x2.x}")
else:
    print("No optimal solution found.")

```