To solve the given problem, we first need to define the variables and then express the objective function and constraints using these variables.

Let's denote:
- $x_1$ as the number of strips of bacon,
- $x_2$ as the number of hamburgers,
- $x_3$ as the number of eggs,
- $x_4$ as the number of tomatoes,
- $x_5$ as the number of kiwis,
- $x_6$ as the number of green beans.

Given the problem description, we are looking to optimize a system with multiple constraints but without an explicit objective function. Since no specific objective is mentioned (like minimizing or maximizing something), and given the nature of the constraints which include both lower and upper bounds on various combinations of these items, it seems like the goal might be to find a feasible solution that satisfies all constraints rather than optimizing for a particular objective.

However, without a clear objective function (e.g., minimize cost, maximize nutritional value), we'll focus on setting up the symbolic representation as requested and then proceed with an example implementation in Gurobi, assuming a simple objective function for demonstration purposes, such as minimizing the total amount of food items.

The symbolic representation would be:
```json
{
    'sym_variables': [
        ('x1', 'strips of bacon'), 
        ('x2', 'hamburgers'), 
        ('x3', 'eggs'), 
        ('x4', 'tomatoes'), 
        ('x5', 'kiwis'), 
        ('x6', 'green beans')
    ], 
    'objective_function': 'Minimize x1 + x2 + x3 + x4 + x5 + x6',
    'constraints': [
        # Umami constraints and others, example:
        '7*x3 - 9*x5 >= 0',
        '-7*x1 + 10*x5 >= 0',
        # Add all other constraints here, following the format
    ]
}
```

Now, let's implement this in Gurobi. We'll need to define the model, variables, objective function, and constraints.

```python
from gurobipy import *

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

# Create variables
x1 = m.addVar(name="strips_of_bacon")
x2 = m.addVar(name="hamburgers")
x3 = m.addVar(name="eggs")
x4 = m.addVar(name="tomatoes")
x5 = m.addVar(name="kiwis")
x6 = m.addVar(name="green_beans")

# Set the objective function to minimize the total amount of food
m.setObjective(x1 + x2 + x3 + x4 + x5 + x6, GRB.MINIMIZE)

# Add constraints, example:
m.addConstr(7*x3 - 9*x5 >= 0, name="eggs_kiwis_constraint")
m.addConstr(-7*x1 + 10*x5 >= 0, name="bacon_kiwis_constraint")

# Umami and protein constraints would be added similarly
# For demonstration, let's assume we have a constraint on the total umami index of bacon and kiwis
m.addConstr(x1 * 20 + x5 * 30 <= 202, name="umami_bacon_kiwis")  # Example umami values

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    for v in m.getVars():
        print(f"{v.varName}: {v.x}")
else:
    print("No optimal solution found")
```