## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to minimize the cost of buying two supplements, A and B, while meeting the patient's requirements for calcium, vitamin A, and vitamin B.

### Define the Variables

Let \(x\) be the number of supplements A to buy, and \(y\) be the number of supplements B to buy.

### Objective Function

The objective is to minimize the total cost, given by \(3.50x + 3.80y\).

### Constraints

1. Calcium: \(3x + 4y \geq 25\)
2. Vitamin A: \(2x + y \geq 20\)
3. Vitamin B: \(3x + 2y \geq 18\)
4. Non-negativity: \(x \geq 0, y \geq 0\)
5. Since we cannot buy fractions of a supplement, \(x\) and \(y\) should be integers.

However, for the purpose of solving this with Gurobi using linear programming (which assumes continuous variables), we will first solve it as a continuous problem and then consider how to handle the integrality constraint.

### Gurobi Code

```python
import gurobi

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

    # Define the variables
    x = model.addVar(name="Supplement_A", lb=0)  # Number of Supplement A
    y = model.addVar(name="Supplement_B", lb=0)  # Number of Supplement B

    # Objective function: Minimize cost
    model.setObjective(3.50 * x + 3.80 * y, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(3 * x + 4 * y >= 25, name="Calcium_Requirement")
    model.addConstr(2 * x + y >= 20, name="Vitamin_A_Requirement")
    model.addConstr(3 * x + 2 * y >= 18, name="Vitamin_B_Requirement")

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal Cost: ${model.objVal:.2f}")
        print(f"Buy {x.varValue:.2f} of Supplement A and {y.varValue:.2f} of Supplement B")
    else:
        print("The model is infeasible")

solve_supplement_problem()
```

### Handling Integrality

If the solution obtained for \(x\) and \(y\) are not integers, and you need an integer solution, you would need to add integrality constraints to the variables:

```python
x = model.addVar(name="Supplement_A", lb=0, vtype=gurobi.GRB.INTEGER)
y = model.addVar(name="Supplement_B", lb=0, vtype=gurobi.GRB.INTEGER)
```

This changes the problem to a Mixed-Integer Linear Programming (MILP) problem, which can be more computationally intensive to solve than a linear programming problem.