## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'ham sandwiches' and 'blueberry pies', which we can denote as $x_1$ and $x_2$ respectively. The objective function to maximize is $3.97x_1 + 1.71x_2$. The constraints are:
- $4.09x_1 + 3.56x_2 \geq 79$ (carbohydrates)
- $3.68x_1 + 0.65x_2 \geq 73$ (fat)
- $5.03x_1 + 5.33x_2 \geq 57$ (tastiness rating)
- $-8x_1 + 7x_2 \geq 0$ (relationship between ham sandwiches and blueberry pies)
- $4.09x_1 + 3.56x_2 \leq 227$ (carbohydrates upper bound)
- $3.68x_1 + 0.65x_2 \leq 120$ (fat upper bound)
- $5.03x_1 + 5.33x_2 \leq 173$ (tastiness rating upper bound)
- $x_2$ is an integer (blueberry pies cannot be a fraction)
- $x_1$ is a continuous variable (ham sandwiches do not have to be an integer)

## Step 2: Convert the problem into a Gurobi-compatible format
We need to define the variables, the objective function, and the constraints in a way that Gurobi can understand.

## 3: Write down the symbolic representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'ham sandwiches'), ('x2', 'blueberry pies')],
    'objective_function': '3.97*x1 + 1.71*x2',
    'constraints': [
        '4.09*x1 + 3.56*x2 >= 79',
        '3.68*x1 + 0.65*x2 >= 73',
        '5.03*x1 + 5.33*x2 >= 57',
        '-8*x1 + 7*x2 >= 0',
        '4.09*x1 + 3.56*x2 <= 227',
        '3.68*x1 + 0.65*x2 <= 120',
        '5.03*x1 + 5.33*x2 <= 173'
    ]
}
```

## 4: Implement the problem in Gurobi
Now, let's implement this problem using Gurobi in Python.

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="ham_sandwiches", lb=0)  # Ham sandwiches
    x2 = model.addVar(name="blueberry_pies", lb=0, integrality=1)  # Blueberry pies

    # Define the objective function
    model.setObjective(3.97 * x1 + 1.71 * x2, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(4.09 * x1 + 3.56 * x2 >= 79, name="carbohydrates_min")
    model.addConstr(3.68 * x1 + 0.65 * x2 >= 73, name="fat_min")
    model.addConstr(5.03 * x1 + 5.33 * x2 >= 57, name="tastiness_min")
    model.addConstr(-8 * x1 + 7 * x2 >= 0, name="relationship")
    model.addConstr(4.09 * x1 + 3.56 * x2 <= 227, name="carbohydrates_max")
    model.addConstr(3.68 * x1 + 0.65 * x2 <= 120, name="fat_max")
    model.addConstr(5.03 * x1 + 5.33 * x2 <= 173, name="tastiness_max")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Ham sandwiches: {x1.varValue}")
        print(f"Blueberry pies: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```