To solve Daniel's problem, we need to formulate a linear programming model that captures his requirements and minimizes the cost. Let's break down the problem:

- Decision variables: Let $Z$ be the amount (in grams) of Zeta supplementation used and $P$ be the amount (in grams) of Phi supplementation used.
- Objective function: The total cost to minimize is given by $0.08Z + 0.18P$, since Zeta costs $0.08 per gram and Phi costs $0.18 per gram.
- Constraints:
  - Iron requirement: $0.15Z + 0.20P \geq 25$ (since Zeta contains 15% iron and Phi contains 20% iron, and Daniel needs at least 25 grams of iron).
  - Vitamin A requirement: $0.20Z + 0.45P \geq 40$ (since Zeta contains 20% vitamin A and Phi contains 45% vitamin A, and Daniel needs at least 40 grams of vitamin A).
  - Non-negativity constraints: $Z \geq 0$ and $P \geq 0$, as the amounts of supplementation cannot be negative.

Here's how we can translate this into Gurobi code in Python:

```python
from gurobipy import *

# Create a model
m = Model("Daniel_Supplementation")

# Decision variables
Z = m.addVar(lb=0, name="Zeta_Supplementation")
P = m.addVar(lb=0, name="Phi_Supplementation")

# Objective function: Minimize total cost
m.setObjective(0.08*Z + 0.18*P, GRB.MINIMIZE)

# Constraints
m.addConstr(0.15*Z + 0.20*P >= 25, name="Iron_Requirement")
m.addConstr(0.20*Z + 0.45*P >= 40, name="VitaminA_Requirement")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Zeta supplementation: {Z.x} grams")
    print(f"Phi supplementation: {P.x} grams")
    print(f"Total cost: ${0.08*Z.x + 0.18*P.x}")
else:
    print("No optimal solution found.")
```