To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints.

Let's define:
- $x_0$ as the number of protein bars,
- $x_1$ as the number of ham sandwiches.

The objective function is to maximize: $5.24x_0 + 6.19x_1$

Constraints are:
1. Umami index constraint (lower bound): $26x_0 + 3x_1 \geq 47$
2. Iron milligrams constraint (lower bound): $25x_0 + 16x_1 \geq 66$
3. Constraint on protein bars and ham sandwiches: $x_0 - 7x_1 \geq 0$
4. Umami index constraint (upper bound): $26x_0 + 3x_1 \leq 72$
5. Iron milligrams constraint (upper bound): $25x_0 + 16x_1 \leq 121$

Since both variables represent quantities of items, they must be non-negative integers.

Here is the symbolic representation in JSON format:
```json
{
    'sym_variables': [('x0', 'protein bars'), ('x1', 'ham sandwiches')],
    'objective_function': '5.24*x0 + 6.19*x1',
    'constraints': [
        '26*x0 + 3*x1 >= 47',
        '25*x0 + 16*x1 >= 66',
        'x0 - 7*x1 >= 0',
        '26*x0 + 3*x1 <= 72',
        '25*x0 + 16*x1 <= 121'
    ]
}
```

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

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

# Define variables
x0 = model.addVar(vtype=GRB.INTEGER, name="protein_bars")
x1 = model.addVar(vtype=GRB.INTEGER, name="ham_sandwiches")

# Set the objective function
model.setObjective(5.24*x0 + 6.19*x1, GRB.MAXIMIZE)

# Add constraints
model.addConstr(26*x0 + 3*x1 >= 47, "umami_index_lower")
model.addConstr(25*x0 + 16*x1 >= 66, "iron_milligrams_lower")
model.addConstr(x0 - 7*x1 >= 0, "protein_bars_ham_sandwiches")
model.addConstr(26*x0 + 3*x1 <= 72, "umami_index_upper")
model.addConstr(25*x0 + 16*x1 <= 121, "iron_milligrams_upper")

# Optimize the model
model.optimize()

# Print the solution
if model.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Protein bars: {x0.x}")
    print(f"Ham sandwiches: {x1.x}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found")
```