To solve the optimization problem described, we will use Gurobi, a powerful tool for solving linear and mixed-integer programming problems. The problem involves maximizing an objective function that depends on the quantities of 'apple pies' and 'blueberry pies', subject to various constraints related to fiber content, protein content, cost, iron content, tastiness rating, and additional linear inequalities.

The variables in this problem are:
- \(x_0\): Quantity of apple pies
- \(x_1\): Quantity of blueberry pies

The objective function to maximize is: \(4.17x_0 + 6.08x_1\)

Constraints based on the problem description are:
1. Fiber content: \(3.95x_0 + 6.48x_1 \geq 73\) and \(3.95x_0 + 6.48x_1 \leq 83\)
2. Protein content: \(12.08x_0 + 1.48x_1 \geq 58\) and \(12.08x_0 + 1.48x_1 \leq 172\)
3. Cost: \(13.27x_0 + 7.25x_1 \geq 56\) and \(13.27x_0 + 7.25x_1 \leq 218\)
4. Iron content: \(12.13x_0 + 12.43x_1 \geq 38\) and \(12.13x_0 + 12.43x_1 \leq 89\)
5. Tastiness rating: \(12.81x_0 + 2.93x_1 \geq 94\) and \(12.81x_0 + 2.93x_1 \leq 119\)
6. Additional linear constraint: \(5x_0 - 4x_1 \geq 0\)

Given that both \(x_0\) and \(x_1\) must be integers, we have a mixed-integer linear programming (MILP) problem.

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="apple_pies")
x1 = m.addVar(vtype=GRB.INTEGER, name="blueberry_pies")

# Objective function: Maximize 4.17*x0 + 6.08*x1
m.setObjective(4.17*x0 + 6.08*x1, GRB.MAXIMIZE)

# Constraints
m.addConstr(3.95*x0 + 6.48*x1 >= 73, name="fiber_min")
m.addConstr(3.95*x0 + 6.48*x1 <= 83, name="fiber_max")
m.addConstr(12.08*x0 + 1.48*x1 >= 58, name="protein_min")
m.addConstr(12.08*x0 + 1.48*x1 <= 172, name="protein_max")
m.addConstr(13.27*x0 + 7.25*x1 >= 56, name="cost_min")
m.addConstr(13.27*x0 + 7.25*x1 <= 218, name="cost_max")
m.addConstr(12.13*x0 + 12.43*x1 >= 38, name="iron_min")
m.addConstr(12.13*x0 + 12.43*x1 <= 89, name="iron_max")
m.addConstr(12.81*x0 + 2.93*x1 >= 94, name="tastiness_min")
m.addConstr(12.81*x0 + 2.93*x1 <= 119, name="tastiness_max")
m.addConstr(5*x0 - 4*x1 >= 0, name="additional_constraint")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Apple Pies: {x0.x}")
    print(f"Blueberry Pies: {x1.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```