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 in algebraic terms.

### Symbolic Representation:

Let's define:
- $x_1$ as the quantity of bowls of pasta,
- $x_2$ as the quantity of black beans.

The objective function to maximize is: $3x_1 + 8x_2$

Constraints are as follows:
1. Umami index constraint (lower bound): $5x_1 + 16x_2 \geq 12$
2. Iron content constraint (lower bound): $8x_1 + 12x_2 \geq 11$
3. Linear combination constraint: $-4x_1 + 10x_2 \geq 0$
4. Umami index constraint (upper bound): $5x_1 + 16x_2 \leq 57$
5. Iron content constraint (upper bound): $8x_1 + 12x_2 \leq 27$

### Symbolic Representation in JSON Format:
```json
{
    'sym_variables': [('x1', 'bowls of pasta'), ('x2', 'black beans')],
    'objective_function': '3*x1 + 8*x2',
    'constraints': [
        '5*x1 + 16*x2 >= 12',
        '8*x1 + 12*x2 >= 11',
        '-4*x1 + 10*x2 >= 0',
        '5*x1 + 16*x2 <= 57',
        '8*x1 + 12*x2 <= 27'
    ]
}
```

### Gurobi Code:
Now, let's write the Gurobi code in Python to solve this optimization problem. We will use the `gurobipy` library for this purpose.

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="bowls_of_pasta")
x2 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="black_beans")

# Set the objective function
m.setObjective(3*x1 + 8*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x1 + 16*x2 >= 12, name="umami_index_lower_bound")
m.addConstr(8*x1 + 12*x2 >= 11, name="iron_content_lower_bound")
m.addConstr(-4*x1 + 10*x2 >= 0, name="linear_combination_constraint")
m.addConstr(5*x1 + 16*x2 <= 57, name="umami_index_upper_bound")
m.addConstr(8*x1 + 12*x2 <= 27, name="iron_content_upper_bound")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"bowls_of_pasta: {x1.x}")
    print(f"black_beans: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```