## Step 1: Define the symbolic representation of the variables
The variables are 'corn cobs' and 'cherry pies', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to maximize is $7.91x_1 + 4.62x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- $20x_1 + 16x_2 \geq 56$ (at least 56 grams of fat)
- $15x_1 + 16x_2 \geq 39$ (total sourness index at least 39)
- $16x_1 + 15x_2 \geq 25$ (at least 25 milligrams of calcium)
- $-3x_1 + 9x_2 \geq 0$ (linear constraint)
- $20x_1 + 16x_2 \leq 101$ (up to 101 grams of fat)
- $15x_1 + 16x_2 \leq 47$ (total sourness index at most 47)
- $16x_1 + 15x_2 \leq 97$ (up to 97 milligrams of calcium)

## 4: Consider the variable bounds
- $x_1$ can be a non-integer number of corn cobs.
- $x_2$ must be a whole number of cherry pies.

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

## 6: Implement the problem using Gurobi
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="corn_cobs", lb=0)  # Non-integer number of corn cobs
    x2 = model.addVar(name="cherry_pies", lb=0, integrality=1)  # Whole number of cherry pies

    # Define the objective function
    model.setObjective(7.91 * x1 + 4.62 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(20 * x1 + 16 * x2 >= 56)  # at least 56 grams of fat
    model.addConstr(15 * x1 + 16 * x2 >= 39)  # total sourness index at least 39
    model.addConstr(16 * x1 + 15 * x2 >= 25)  # at least 25 milligrams of calcium
    model.addConstr(-3 * x1 + 9 * x2 >= 0)  # linear constraint
    model.addConstr(20 * x1 + 16 * x2 <= 101)  # up to 101 grams of fat
    model.addConstr(15 * x1 + 16 * x2 <= 47)  # total sourness index at most 47
    model.addConstr(16 * x1 + 15 * x2 <= 97)  # up to 97 milligrams of calcium

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```