## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to minimize the cost of two supplements, A and B, while meeting the daily requirements of keratin and calcium.

### Decision Variables

Let $x$ be the number of servings of supplement A and $y$ be the number of servings of supplement B.

### Objective Function

The objective is to minimize the total cost, which is $2x + 4y$.

### Constraints

1. **Keratin Requirement**: The man needs at least 12 units of keratin. Since supplement A contains 1 unit of keratin per serving and supplement B contains 4 units of keratin per serving, the constraint is $x + 4y \geq 12$.
2. **Calcium Requirement**: The man needs at least 20 units of calcium. Since supplement A contains 5 units of calcium per serving and supplement B contains 1 unit of calcium per serving, the constraint is $5x + y \geq 20$.
3. **Non-Negativity**: The number of servings of each supplement cannot be negative, so $x \geq 0$ and $y \geq 0$.

### Gurobi Code

```python
import gurobi

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

    # Define the decision variables
    x = model.addVar(lb=0, name="servings_of_supplement_A")
    y = model.addVar(lb=0, name="servings_of_supplement_B")

    # Define the objective function
    model.setObjective(2*x + 4*y, gurobi.GRB.MINIMIZE)

    # Define the constraints
    model.addConstr(x + 4*y >= 12, name="keratin_requirement")
    model.addConstr(5*x + y >= 20, name="calcium_requirement")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal servings of supplement A: {x.varValue}")
        print(f"Optimal servings of supplement B: {y.varValue}")
        print(f"Minimum cost: {model.objVal}")
    else:
        print("The problem is infeasible.")

solve_supplement_problem()
```

This code defines the optimization problem using Gurobi's Python interface, solves it, and prints the optimal solution. If the problem is infeasible, it indicates that there is no solution that satisfies all the constraints.