To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints algebraically.

Let's define:
- $x_1$ as the number of servings of carrot juice.
- $x_2$ as the number of servings of lemon juice.

The objective is to minimize the total cost, which can be represented by the objective function: $3.5x_1 + 6x_2$.

The constraints are:
1. Vitamin A requirement: $8x_1 + 3x_2 \geq 25$
2. Vitamin B requirement: $3x_1 + 6x_2 \geq 25$
3. Non-negativity constraint for both variables since we cannot have a negative number of servings: $x_1, x_2 \geq 0$

The symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'carrot juice'), ('x2', 'lemon juice')],
    'objective_function': '3.5*x1 + 6*x2',
    'constraints': ['8*x1 + 3*x2 >= 25', '3*x1 + 6*x2 >= 25', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="carrot_juice")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="lemon_juice")

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

# Add constraints
m.addConstr(8*x1 + 3*x2 >= 25, "Vitamin_A_Requirement")
m.addConstr(3*x1 + 6*x2 >= 25, "Vitamin_B_Requirement")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Carrot juice servings: {x1.x}")
    print(f"Lemon juice servings: {x2.x}")
    print(f"Total cost: ${3.5*x1.x + 6*x2.x:.2f}")
else:
    print("No optimal solution found")
```