## Step 1: Define the symbolic representation of the variables
The variables are 'knishes' and 'sashimi', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The objective function to maximize is $3.68x_1 + 3.44x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $3x_1 + 6x_2 \geq 49$ (umami index)
- $x_1 + 4x_2 \geq 68$ (healthiness rating)
- $4x_1 - 5x_2 \geq 0$ (knishes and sashimi mix)
- $3x_1 + 6x_2 \leq 84$ (umami index upper bound)
- $x_1 + 4x_2 \leq 165$ (healthiness rating upper bound)

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'knishes'), ('x2', 'sashimi')], 
    'objective_function': '3.68*x1 + 3.44*x2', 
    'constraints': [
        '3*x1 + 6*x2 >= 49', 
        'x1 + 4*x2 >= 68', 
        '4*x1 - 5*x2 >= 0', 
        '3*x1 + 6*x2 <= 84', 
        'x1 + 4*x2 <= 165'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
knishes = model.addVar(name='knishes', lb=0)  # Fractional amount allowed
sashimi = model.addVar(name='sashimi', lb=0)  # Fractional amount allowed

# Define the objective function
model.setObjective(3.68 * knishes + 3.44 * sashimi, gurobi.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(3 * knishes + 6 * sashimi >= 49, name='umami_index_min')
model.addConstr(knishes + 4 * sashimi >= 68, name='healthiness_rating_min')
model.addConstr(4 * knishes - 5 * sashimi >= 0, name='knishes_sashimi_mix')
model.addConstr(3 * knishes + 6 * sashimi <= 84, name='umami_index_max')
model.addConstr(knishes + 4 * sashimi <= 165, name='healthiness_rating_max')

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print('Optimal solution found.')
    print(f'Knishes: {knishes.varValue}')
    print(f'Sashimi: {sashimi.varValue}')
    print(f'Objective: {model.objVal}')
else:
    print('No optimal solution found.')
```