To solve the given optimization problem, we first need to define the variables and the objective function, followed by the constraints. The problem involves minimizing an objective function subject to several constraints.

## Step 1: Define the Variables
Let's define the variables as follows:
- `x0`: grams of fiber
- `x1`: milligrams of vitamin B3
- `x2`: milligrams of iron

## 2: Define the Objective Function
The objective function to minimize is: `4*x0 + 5*x1 + 6*x2`

## 3: Define the Constraints
Given constraints:
- `5*x0 + 3*x1 + 8*x2 <= 55` (total energy stability index)
- `3*x1 + 8*x2 >= 13` (combined index from B3 and iron)
- `5*x0 + 3*x1 >= 14` (combined index from fiber and B3)
- `5*x0 + 3*x1 + 8*x2 >= 14` (combined index from all)
- `-10*x0 + 7*x2 >= 0` (relationship between fiber and iron)
- `-7*x1 + 9*x2 >= 0` (relationship between B3 and iron)
- `5*x0 + 3*x1 <= 49` (combined index from fiber and B3, upper limit)
- `3*x1 + 8*x2 <= 51` (combined index from B3 and iron, upper limit)

## 4: Implement in Gurobi
We will use Gurobi's Python API to model and solve this problem.

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x0 = m.addVar(name="grams_of_fiber", lb=0)  # No upper bound given
x1 = m.addVar(name="milligrams_of_vitamin_B3", lb=0)  # No upper bound given
x2 = m.addVar(name="milligrams_of_iron", lb=0)  # No upper bound given

# Objective function
m.setObjective(4*x0 + 5*x1 + 6*x2, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(5*x0 + 3*x1 + 8*x2 <= 55, name="energy_stability_index")
m.addConstr(3*x1 + 8*x2 >= 13, name="B3_iron_index")
m.addConstr(5*x0 + 3*x1 >= 14, name="fiber_B3_index")
m.addConstr(5*x0 + 3*x1 + 8*x2 >= 14, name="all_index")
m.addConstr(-10*x0 + 7*x2 >= 0, name="fiber_iron_relationship")
m.addConstr(-7*x1 + 9*x2 >= 0, name="B3_iron_relationship")
m.addConstr(5*x0 + 3*x1 <= 49, name="fiber_B3_upper_limit")
m.addConstr(3*x1 + 8*x2 <= 51, name="B3_iron_upper_limit")

# Optimize the model
m.optimize()

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