## Step 1: Define the symbolic representation of the variables
The variables are 'sashimi', 'bagged salads', 'hamburgers', and 'black beans', which can be represented symbolically as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $5.74x_1 + 6.64x_2 + 4.51x_3 + 4.14x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
1. $4x_2 + 3x_3 + 10x_4 \geq 17$
2. $4x_2 + 10x_4 \leq 38$
3. $5x_1 + 10x_4 \leq 37$
4. $3x_3 + 10x_4 \leq 62$
5. $5x_1 + 4x_2 \leq 74$
6. $5x_1 + 4x_2 + 10x_4 \leq 71$
7. $5x_1 + 4x_2 + 3x_3 + 10x_4 \leq 71$

## 4: Specify the variable bounds and types
- $x_1, x_2, x_3$ can be non-integer (float)
- $x_4$ must be an integer

## 5: Create the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'sashimi'), ('x2', 'bagged salads'), ('x3', 'hamburgers'), ('x4', 'black beans')],
'objective_function': '5.74*x1 + 6.64*x2 + 4.51*x3 + 4.14*x4',
'constraints': [
'4*x2 + 3*x3 + 10*x4 >= 17',
'4*x2 + 10*x4 <= 38',
'5*x1 + 10*x4 <= 37',
'3*x3 + 10*x4 <= 62',
'5*x1 + 4*x2 <= 74',
'5*x1 + 4*x2 + 10*x4 <= 71',
'5*x1 + 4*x2 + 3*x3 + 10*x4 <= 71'
]
}
```

## 6: Write the Gurobi code to solve the optimization problem
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    sashimi = model.addVar(name="sashimi", lb=0)
    bagged_salads = model.addVar(name="bagged_salads", lb=0)
    hamburgers = model.addVar(name="hamburgers", lb=0)
    black_beans = model.addVar(name="black beans", lb=0, vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(5.74 * sashimi + 6.64 * bagged_salads + 4.51 * hamburgers + 4.14 * black_beans, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(4 * bagged_salads + 3 * hamburgers + 10 * black_beans >= 17)
    model.addConstr(4 * bagged_salads + 10 * black_beans <= 38)
    model.addConstr(5 * sashimi + 10 * black_beans <= 37)
    model.addConstr(3 * hamburgers + 10 * black_beans <= 62)
    model.addConstr(5 * sashimi + 4 * bagged_salads <= 74)
    model.addConstr(5 * sashimi + 4 * bagged_salads + 10 * black_beans <= 71)
    model.addConstr(5 * sashimi + 4 * bagged_salads + 3 * hamburgers + 10 * black_beans <= 71)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Sashimi: {sashimi.x}")
        print(f"Bagged Salads: {bagged_salads.x}")
        print(f"Hamburgers: {hamburgers.x}")
        print(f"Black Beans: {black_beans.x}")
        print(f"Objective: {model.objval}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```