## Step 1: Define the symbolic representation of the problem

Let's denote:
- $x_1$ as the amount of white cocktail in kilograms
- $x_2$ as the amount of green cocktail in kilograms

The objects are:
- White cocktail
- Green cocktail

## Step 2: Determine the objective function

The objective is to minimize the cost. The white cocktail costs $5.5 per kilogram and the green cocktail costs $12 per kilogram. Therefore, the objective function is:
\[ \text{Minimize:} \quad 5.5x_1 + 12x_2 \]

## 3: Define the constraints

1. The super cocktail must have a minimum of 5 kilograms of alcohol. The white cocktail has 7% alcohol and the green cocktail has 2% alcohol. Therefore:
\[ 0.07x_1 + 0.02x_2 \geq 5 \]

2. The super cocktail must have a minimum of 25 kilograms of sugar. The white cocktail has 10% sugar and the green cocktail has 25% sugar. Therefore:
\[ 0.10x_1 + 0.25x_2 \geq 25 \]

3. The amounts of cocktails cannot be negative:
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

## 4: Symbolic representation in JSON format

```json
{
    'sym_variables': [('x1', 'white cocktail'), ('x2', 'green cocktail')],
    'objective_function': '5.5*x1 + 12*x2',
    'constraints': [
        '0.07*x1 + 0.02*x2 >= 5',
        '0.10*x1 + 0.25*x2 >= 25',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 5: Gurobi code in Python

```python
import gurobipy as gp

# Create a new model
m = gp.Model("Cocktail_Mixing")

# Define variables
x1 = m.addVar(name="white_cocktail", lb=0)  # Amount of white cocktail
x2 = m.addVar(name="green_cocktail", lb=0)  # Amount of green cocktail

# Objective function: minimize cost
m.setObjective(5.5 * x1 + 12 * x2, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(0.07 * x1 + 0.02 * x2 >= 5, name="alcohol_constraint")
m.addConstr(0.10 * x1 + 0.25 * x2 >= 25, name="sugar_constraint")

# Solve the model
m.solve()

# Print the results
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Amount of white cocktail: {x1.varValue} kg")
    print(f"Amount of green cocktail: {x2.varValue} kg")
    print(f"Minimum cost: ${m.objVal:.2f}")
else:
    print("No optimal solution found.")
```