To tackle this optimization problem, we first need to break down the given information into a symbolic representation. This involves defining variables for each item (cheeseburgers and bowls of cereal), formulating the objective function using these variables, and then listing all constraints in terms of these variables.

Given:
- Variables: `x0` for cheeseburgers, `x1` for bowls of cereal.
- Objective Function: Minimize `9.54*x0 + 3.68*x1`.
- Constraints:
  - Iron constraint: `2*x0 + 6*x1 >= 52` and `2*x0 + 6*x1 <= 67`.
  - Umami index constraints: `11*x0 + 7*x1 >= 20` and `11*x0 + 7*x1 <= 28`.
  - Healthiness rating constraints: `16*x0 + 16*x1 >= 26` and `16*x0 + 16*x1 <= 53`.
  - Tastiness rating constraint: `7*x0 + 5*x1 >= 44` and `7*x0 + 5*x1 <= 77`.
  - Additional linear constraint: `-2*x0 + 3*x1 >= 0`.

Now, let's represent the problem symbolically:

```json
{
  'sym_variables': [('x0', 'cheeseburgers'), ('x1', 'bowls of cereal')],
  'objective_function': '9.54*x0 + 3.68*x1',
  'constraints': [
    '2*x0 + 6*x1 >= 52',
    '2*x0 + 6*x1 <= 67',
    '11*x0 + 7*x1 >= 20',
    '11*x0 + 7*x1 <= 28',
    '16*x0 + 16*x1 >= 26',
    '16*x0 + 16*x1 <= 53',
    '7*x0 + 5*x1 >= 44',
    '7*x0 + 5*x1 <= 77',
    '-2*x0 + 3*x1 >= 0'
  ]
}
```

Next, we'll write the Gurobi code to solve this optimization problem. We need to ensure that both `x0` and `x1` are integers since they represent whole numbers of items.

```python
from gurobipy import *

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

# Define variables as integers
x0 = m.addVar(vtype=GRB.INTEGER, name="cheeseburgers")
x1 = m.addVar(vtype=GRB.INTEGER, name="bowls_of_cereal")

# Set the objective function
m.setObjective(9.54*x0 + 3.68*x1, GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x0 + 6*x1 >= 52, "iron_min")
m.addConstr(2*x0 + 6*x1 <= 67, "iron_max")
m.addConstr(11*x0 + 7*x1 >= 20, "umami_min")
m.addConstr(11*x0 + 7*x1 <= 28, "umami_max")
m.addConstr(16*x0 + 16*x1 >= 26, "healthiness_min")
m.addConstr(16*x0 + 16*x1 <= 53, "healthiness_max")
m.addConstr(7*x0 + 5*x1 >= 44, "tastiness_min")
m.addConstr(7*x0 + 5*x1 <= 77, "tastiness_max")
m.addConstr(-2*x0 + 3*x1 >= 0, "additional_constraint")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Cheeseburgers: {x0.x}")
    print(f"Bowls of cereal: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```