To solve the given problem, we first need to translate the natural language description into a symbolic representation. Let's define:

- $x_1$ as the number of servings of grains eaten every day.
- $x_2$ as the number of servings of vegetables eaten every day.

The objective function aims to minimize the total cost of eating these food groups, which can be represented as:
\[0.40x_1 + 0.60x_2\]

The constraints are based on the daily requirements for iron and fiber:
- At least 100 grams of iron: $30x_1 + 15x_2 \geq 100$
- At least 150 grams of fiber: $5x_1 + 25x_2 \geq 150$

Also, since we cannot eat a negative number of servings, we have:
- $x_1 \geq 0$
- $x_2 \geq 0$

Symbolic representation in JSON format:
```json
{
    'sym_variables': [('x1', 'number of servings of grains'), ('x2', 'number of servings of vegetables')],
    'objective_function': '0.40*x1 + 0.60*x2',
    'constraints': ['30*x1 + 15*x2 >= 100', '5*x1 + 25*x2 >= 150', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this optimization problem using Gurobi in Python:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="grains", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="vegetables", lb=0)

# Set the objective function
m.setObjective(0.40*x1 + 0.60*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(30*x1 + 15*x2 >= 100, "iron_requirement")
m.addConstr(5*x1 + 25*x2 >= 150, "fiber_requirement")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of servings of grains: {x1.x}")
    print(f"Number of servings of vegetables: {x2.x}")
    print(f"Total cost: ${0.40*x1.x + 0.60*x2.x:.2f}")
else:
    print("No optimal solution found")
```