To solve Andy's problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables as follows:
- $x_1$: Number of bottles of chocolate milk
- $x_2$: Number of bottles of vegetable juice

The objective function is to minimize the total cost, which can be represented algebraically as:
\[3.5x_1 + 6x_2\]

The constraints are:
- Potassium: $6x_1 + 9x_2 \geq 20$
- Magnesium: $4x_1 + 5x_2 \geq 8$
- Calcium: $5x_1 + 7x_2 \geq 12$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$ (since we can't buy a negative number of bottles)

Here is the symbolic representation in JSON format:
```json
{
    'sym_variables': [('x1', 'Number of bottles of chocolate milk'), ('x2', 'Number of bottles of vegetable juice')],
    'objective_function': '3.5*x1 + 6*x2',
    'constraints': ['6*x1 + 9*x2 >= 20', '4*x1 + 5*x2 >= 8', '5*x1 + 7*x2 >= 12', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem using Gurobi in Python:
```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(lb=0, name="chocolate_milk")
x2 = m.addVar(lb=0, name="vegetable_juice")

# Set the objective function
m.setObjective(3.5*x1 + 6*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(6*x1 + 9*x2 >= 20, "potassium")
m.addConstr(4*x1 + 5*x2 >= 8, "magnesium")
m.addConstr(5*x1 + 7*x2 >= 12, "calcium")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of bottles of chocolate milk: {x1.x}")
    print(f"Number of bottles of vegetable juice: {x2.x}")
    print(f"Minimum cost: ${m.objVal:.2f}")
else:
    print("No optimal solution found")
```