To solve Robert's problem, we first need to define the decision variables and the objective function. Let's denote the amount of white cocktail used as \(W\) (in kilograms) and the amount of green cocktail used as \(G\) (in kilograms). The objective is to minimize the total cost, which can be expressed as \(5.5W + 12G\).

The constraints are:
1. The super cocktail must have at least 5 kilograms of alcohol.
2. The super cocktail must have at least 25 kilograms of sugar.

Given that the white cocktail has 7% alcohol and the green cocktail has 2% alcohol, we can express the total amount of alcohol in the super cocktail as \(0.07W + 0.02G \geq 5\).

For sugar, given that the white cocktail has 10% sugar and the green cocktail has 25% sugar, the total amount of sugar in the super cocktail can be expressed as \(0.10W + 0.25G \geq 25\).

We also need to ensure that we cannot use negative amounts of either cocktail, so \(W \geq 0\) and \(G \geq 0\).

Now, let's translate this problem into Gurobi code in Python:

```python
from gurobipy import *

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

# Define the decision variables
W = m.addVar(name="White_Cocktail", vtype=GRB.CONTINUOUS, lb=0)
G = m.addVar(name="Green_Cocktail", vtype=GRB.CONTINUOUS, lb=0)

# Set the objective function: minimize total cost
m.setObjective(5.5*W + 12*G, GRB.MINIMIZE)

# Add constraints
m.addConstr(0.07*W + 0.02*G >= 5, name="Alcohol_Constraint")
m.addConstr(0.10*W + 0.25*G >= 25, name="Sugar_Constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"White Cocktail: {W.x} kg")
    print(f"Green Cocktail: {G.x} kg")
    print(f"Total Cost: ${5.5*W.x + 12*G.x}")
else:
    print("No optimal solution found")

```