## Step 1: Define the symbolic representation of the problem
Let's denote the number of bottles of chocolate milk as $x_1$ and the number of bottles of vegetable juice as $x_2$. The objective is to minimize the total cost, which is $3.5x_1 + 6x_2$. 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: $x_1 \geq 0, x_2 \geq 0$

## 2: Convert the problem into a symbolic representation
The symbolic representation can be described as:
```json
{
    'sym_variables': [('x1', 'chocolate milk'), ('x2', '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'
    ]
}
```

## 3: Implement the problem in Gurobi code
To solve this linear programming problem using Gurobi, we will use the Gurobi Python API.

```python
import gurobi as gp

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

# Define the variables
x1 = m.addVar(name="chocolate_milk", lb=0)  # Number of bottles of chocolate milk
x2 = m.addVar(name="vegetable_juice", lb=0)  # Number of bottles of vegetable juice

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

# Define the constraints
m.addConstr(6 * x1 + 9 * x2 >= 20, name="potassium_constraint")
m.addConstr(4 * x1 + 5 * x2 >= 8, name="magnesium_constraint")
m.addConstr(5 * x1 + 7 * x2 >= 12, name="calcium_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal cost: ${m.objVal:.2f}")
    print(f"Bottles of chocolate milk: {x1.x:.2f}")
    print(f"Bottles of vegetable juice: {x2.x:.2f}")
else:
    print("The model is infeasible.")
```