## Step 1: Define the symbolic representation of the problem
The problem involves finding the optimal number of supplements A and B a patient should buy to minimize cost while meeting certain nutritional requirements. Let's define the symbolic variables:
- $x_1$ represents the number of Supplement A
- $x_2$ represents the number of Supplement B

## Step 2: Translate the objective function into symbolic notation
The objective is to minimize the total cost. The cost of Supplement A is $3.50 per unit, and the cost of Supplement B is $3.80 per unit. Thus, the objective function can be represented as:
\[ \text{Minimize:} \quad 3.50x_1 + 3.80x_2 \]

## 3: Translate the constraints into symbolic notation
The patient must get at least:
- 25 units of calcium: $3x_1 + 4x_2 \geq 25$
- 20 units of vitamin A: $2x_1 + x_2 \geq 20$
- 18 units of vitamin B: $3x_1 + 2x_2 \geq 18$
Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of supplements cannot be negative.

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

## 5: Implement the problem in Gurobi Python
```python
import gurobi

def solve_supplement_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="x1", lb=0, vtype=gurobi.GRB.CONTINUOUS)  # Supplement A
    x2 = model.addVar(name="x2", lb=0, vtype=gurobi.GRB.CONTINUOUS)  # Supplement B

    # Define the objective function
    model.setObjective(3.50 * x1 + 3.80 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(3 * x1 + 4 * x2 >= 25, name="calcium_constraint")
    model.addConstr(2 * x1 + x2 >= 20, name="vitamin_A_constraint")
    model.addConstr(3 * x1 + 2 * x2 >= 18, name="vitamin_B_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Minimum cost: {model.objVal}")
    else:
        print("The problem is infeasible")

solve_supplement_problem()
```