## Problem Description and Formulation

The problem is a linear programming optimization problem. Daniel needs to meet his nutritional requirements for iron and vitamin A by consuming two types of liquid supplementation: Zeta and Phi. The goal is to minimize the cost while meeting the requirements.

### Decision Variables

Let $Z$ be the amount of Zeta supplementation in grams and $\Phi$ be the amount of Phi supplementation in grams.

### Objective Function

The objective is to minimize the total cost, which is given by $0.08Z + 0.18\Phi$.

### Constraints

1. **Iron Requirement**: Zeta supplementation consists of 15% iron, and Phi supplementation consists of 20% iron. Daniel needs a minimum of 25 grams of iron. This can be represented as $0.15Z + 0.20\Phi \geq 25$.
2. **Vitamin A Requirement**: Zeta supplementation consists of 20% vitamin A, and Phi supplementation consists of 45% vitamin A. Daniel needs a minimum of 40 grams of vitamin A. This can be represented as $0.20Z + 0.45\Phi \geq 40$.
3. **Non-Negativity Constraints**: The amount of each supplementation cannot be negative, so $Z \geq 0$ and $\Phi \geq 0$.

## Gurobi Code

```python
import gurobi

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

    # Define the decision variables
    Z = model.addVar(lb=0, name="Zeta")
    Phi = model.addVar(lb=0, name="Phi")

    # Define the objective function
    model.setObjective(0.08 * Z + 0.18 * Phi, gurobi.GRB.MINIMIZE)

    # Add the iron requirement constraint
    model.addConstr(0.15 * Z + 0.20 * Phi >= 25, name="Iron_Requirement")

    # Add the vitamin A requirement constraint
    model.addConstr(0.20 * Z + 0.45 * Phi >= 40, name="Vitamin_A_Requirement")

    # Optimize the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Zeta: {Z.varValue} grams")
        print(f"Phi: {Phi.varValue} grams")
        print(f"Cost: ${model.objVal:.2f}")
    else:
        print("The model is infeasible.")

solve_supplementation_problem()
```

This code defines the optimization problem using Gurobi's Python interface, solves it, and prints out the optimal amounts of Zeta and Phi supplementation and the minimum cost. If the problem is infeasible, it indicates that the requirements cannot be met.