To solve the given optimization problem, we will first define the decision variables and then formulate the objective function and constraints according to the provided description. We'll use Gurobi, a popular linear programming solver, to find the optimal solution.

### Decision Variables:
- Let $x_0$ represent the quantity of grams of fiber.
- Let $x_1$ represent the quantity of milligrams of vitamin B3.
- Let $x_2$ represent the quantity of milligrams of iron.

### Objective Function:
The objective is to minimize $4x_0 + 5x_1 + 6x_2$.

### Constraints:
1. Energy stability index for grams of fiber: $5x_0$
2. Energy stability index for milligrams of vitamin B3: $3x_1$
3. Energy stability index for milligrams of iron: $8x_2$
4. Combined energy stability index from milligrams of vitamin B3 and milligrams of iron $\geq 13$: $3x_1 + 8x_2 \geq 13$
5. Combined energy stability index from grams of fiber and milligrams of vitamin B3 $\geq 14$: $5x_0 + 3x_1 \geq 14$
6. Total combined energy stability index from all $\geq 14$: $5x_0 + 3x_1 + 8x_2 \geq 14$
7. $-10x_0 + 7x_2 \geq 0$
8. $-7x_1 + 9x_2 \geq 0$
9. Combined energy stability index from grams of fiber and milligrams of vitamin B3 $\leq 49$: $5x_0 + 3x_1 \leq 49$
10. Combined energy stability index from milligrams of vitamin B3 and milligrams of iron $\leq 51$: $3x_1 + 8x_2 \leq 51$

All variables ($x_0, x_1, x_2$) are continuous.

Now, let's implement this problem in Gurobi using Python:

```python
from gurobipy import *

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

# Define the decision variables
x0 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="grams_of_fiber")
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B3")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_iron")

# Define the objective function
m.setObjective(4*x0 + 5*x1 + 6*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(3*x1 + 8*x2 >= 13, "vitamin_B3_and_iron_index")
m.addConstr(5*x0 + 3*x1 >= 14, "fiber_and_vitamin_B3_index")
m.addConstr(5*x0 + 3*x1 + 8*x2 >= 14, "total_index")
m.addConstr(-10*x0 + 7*x2 >= 0, "fiber_and_iron_constraint")
m.addConstr(-7*x1 + 9*x2 >= 0, "vitamin_B3_and_iron_constraint")
m.addConstr(5*x0 + 3*x1 <= 49, "fiber_and_vitamin_B3_index_max")
m.addConstr(3*x1 + 8*x2 <= 51, "vitamin_B3_and_iron_index_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Grams of fiber: {x0.x}")
    print(f"Milligrams of vitamin B3: {x1.x}")
    print(f"Milligrams of iron: {x2.x}")
else:
    print("No optimal solution found")
```