To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables for each item ('knishes' and 'sashimi'), formulating the objective function using these variables, and then translating all constraints into algebraic expressions.

### Symbolic Representation
Let's define:
- $x_1$ as the quantity of knishes,
- $x_2$ as the quantity of sashimi.

The objective function to maximize is: $3.68x_1 + 3.44x_2$

Given constraints:
1. Umami index constraint: $3x_1 + 6x_2 \geq 49$
2. Healthiness rating constraint: $1x_1 + 4x_2 \geq 68$
3. Mixed constraint: $4x_1 - 5x_2 \geq 0$
4. Upper bound on umami index: $3x_1 + 6x_2 \leq 84$
5. Upper bound on healthiness rating: $1x_1 + 4x_2 \leq 165$

### Symbolic Representation in JSON Format
```json
{
    'sym_variables': [('x1', 'knishes'), ('x2', 'sashimi')],
    'objective_function': '3.68*x1 + 3.44*x2',
    'constraints': [
        '3*x1 + 6*x2 >= 49',
        '1*x1 + 4*x2 >= 68',
        '4*x1 - 5*x2 >= 0',
        '3*x1 + 6*x2 <= 84',
        '1*x1 + 4*x2 <= 165'
    ]
}
```

### Gurobi Code
To implement this problem in Gurobi, we use Python. We need to import the Gurobi library and then define our variables, objective function, and constraints accordingly.

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, name="knishes")
x2 = m.addVar(lb=0, name="sashimi")

# Set the objective function
m.setObjective(3.68*x1 + 3.44*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x1 + 6*x2 >= 49, "umami_index_lower")
m.addConstr(1*x1 + 4*x2 >= 68, "healthiness_rating_lower")
m.addConstr(4*x1 - 5*x2 >= 0, "mixed_constraint")
m.addConstr(3*x1 + 6*x2 <= 84, "umami_index_upper")
m.addConstr(1*x1 + 4*x2 <= 165, "healthiness_rating_upper")

# Optimize model
m.optimize()

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