To solve the problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the given information.

Let's define:
- $x_1$ as the number of Supplement A purchased,
- $x_2$ as the number of Supplement B purchased.

The objective is to minimize the total cost, which can be represented as $3.50x_1 + 3.80x_2$.

The constraints based on the nutritional requirements are:
1. Calcium: $3x_1 + 4x_2 \geq 25$
2. Vitamin A: $2x_1 + x_2 \geq 20$
3. Vitamin B: $3x_1 + 2x_2 \geq 18$

Additionally, since the number of supplements cannot be negative, we have:
4. $x_1 \geq 0$
5. $x_2 \geq 0$

Symbolic representation in JSON format:
```json
{
    'sym_variables': [('x1', 'Supplement A'), ('x2', 'Supplement B')],
    'objective_function': '3.50*x1 + 3.80*x2',
    'constraints': [
        '3*x1 + 4*x2 >= 25',
        '2*x1 + x2 >= 20',
        '3*x1 + 2*x2 >= 18',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

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

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(3.50*x1 + 3.80*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(3*x1 + 4*x2 >= 25, "Calcium_Requirement")
m.addConstr(2*x1 + x2 >= 20, "Vitamin_A_Requirement")
m.addConstr(3*x1 + 2*x2 >= 18, "Vitamin_B_Requirement")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Supplement A: {x1.x}")
    print(f"Supplement B: {x2.x}")
    print(f"Total Cost: ${3.50*x1.x + 3.80*x2.x:.2f}")
else:
    print("No optimal solution found")
```