To solve this problem, we first need to define the decision variables and the objective function. Let's denote the number of servings of grains as `G` and the number of servings of vegetables as `V`. The objective is to minimize the total cost, which can be calculated as `0.40G + 0.60V`.

The constraints are based on the daily requirements for iron and fiber:
1. For iron: `15V + 30G >= 100`
2. For fiber: `25V + 5G >= 150`

Additionally, since we cannot eat a negative number of servings, both `G` and `V` must be non-negative.

Here is the reasoning behind translating these constraints into Gurobi code:

- We will use the `gurobipy` library in Python to model and solve this linear programming problem.
- The decision variables `G` and `V` will be modeled as continuous variables, but since we are dealing with servings of food, in practice, they should be integers. However, for simplicity and because the problem does not explicitly state that fractional servings are not allowed, we'll treat them as continuous first.
- We define the model, add the decision variables, set up the objective function to minimize cost, and then add the constraints for iron and fiber intake.

```python
from gurobipy import *

# Create a new model
m = Model("Food_Optimization")

# Define the decision variables
G = m.addVar(lb=0, name="Grains")
V = m.addVar(lb=0, name="Vegetables")

# Set the objective function to minimize cost
m.setObjective(0.40*G + 0.60*V, GRB.MINIMIZE)

# Add constraints for iron and fiber requirements
m.addConstr(15*V + 30*G >= 100, "Iron_Requirement")
m.addConstr(25*V + 5*G >= 150, "Fiber_Requirement")

# Optimize the model
m.optimize()

# Print out the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Grains: {G.x}")
    print(f"Vegetables: {V.x}")
    print(f"Total Cost: ${0.40*G.x + 0.60*V.x:.2f}")
else:
    print("No optimal solution found")

```