To solve this problem, we first need to define the variables and the objective function. Let's denote the amount of green apples used as \(x_g\) (in kg) and the amount of red apples used as \(x_r\) (in kg). The objective is to minimize the total cost, which can be represented as \(9x_g + 7x_r\), since green apples cost $9 per kg and red apples cost $7 per kg.

The constraints are based on the sugar and fiber content requirements. For sugar, we need at least 12 kg, so the constraint is \(0.05x_g + 0.25x_r \geq 12\). For fiber, we need at least 5 kg, leading to the constraint \(0.16x_g + 0.08x_r \geq 5\).

Additionally, since we cannot use negative amounts of apples, both \(x_g\) and \(x_r\) must be non-negative.

Now, let's translate this into Gurobi code in Python:

```python
from gurobipy import *

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

# Define the variables
x_g = m.addVar(lb=0, name="green_apples")  # Amount of green apples in kg
x_r = m.addVar(lb=0, name="red_apples")    # Amount of red apples in kg

# Set the objective function: Minimize the total cost
m.setObjective(9*x_g + 7*x_r, GRB.MINIMIZE)

# Add constraints
m.addConstr(0.05*x_g + 0.25*x_r >= 12, name="sugar_constraint")  # Minimum sugar requirement
m.addConstr(0.16*x_g + 0.08*x_r >= 5, name="fiber_constraint")   # Minimum fiber requirement

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Minimum cost: $", m.objVal)
    print("Green apples to use (kg): ", x_g.x)
    print("Red apples to use (kg): ", x_r.x)
else:
    print("The model is infeasible")
```