## Step 1: Define the symbolic representation of the variables
The variables are 'strawberries' and 'milkshakes'. Let's denote 'strawberries' as $x_1$ and 'milkshakes' as $x_2$.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $2.92 \cdot x_1 \cdot x_2 + 2.39 \cdot x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
1. $13x_1 + 4x_2 \geq 20$
2. $11x_1 + 2x_2 \geq 12$
3. $-3x_1 + 9x_2 \geq 0$
4. $13x_1 + 4x_2 \leq 46$
5. $11x_1 + 2x_2 \leq 37$
6. $x_1$ is an integer
7. $x_2$ is a real number

## 4: Create the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'strawberries'), ('x2', 'milkshakes')], 
'objective_function': '2.92 * x1 * x2 + 2.39 * x2', 
'constraints': [
    '13 * x1 + 4 * x2 >= 20', 
    '11 * x1 + 2 * x2 >= 12', 
    '-3 * x1 + 9 * x2 >= 0', 
    '13 * x1 + 4 * x2 <= 46', 
    '11 * x1 + 2 * x2 <= 37', 
    'x1 is an integer'
  ]
}
```

## Step 5: Write the Gurobi code for the optimization problem
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="strawberries", vtype=gurobi.GRB.INTEGER)  # strawberries
    x2 = model.addVar(name="milkshakes")  # milkshakes

    # Define the objective function
    model.setObjective(2.92 * x1 * x2 + 2.39 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(13 * x1 + 4 * x2 >= 20)  # healthiness rating >= 20
    model.addConstr(11 * x1 + 2 * x2 >= 12)  # cost >= 12
    model.addConstr(-3 * x1 + 9 * x2 >= 0)  # -3x1 + 9x2 >= 0
    model.addConstr(13 * x1 + 4 * x2 <= 46)  # healthiness rating <= 46
    model.addConstr(11 * x1 + 2 * x2 <= 37)  # cost <= 37

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Strawberries: {x1.varValue}")
        print(f"Milkshakes: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```