## Step 1: Define the symbolic representation of the variables
The variables are 'postage stamps', 'paper clips', and 'headsets', which we will represent symbolically as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $7.71x_1 + 6.19x_2 + 5.07x_3$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
1. $4.49x_1 \leq 233$
2. $3.37x_2 \leq 233$
3. $1.38x_3 \leq 233$
4. $4.49x_1 + 1.38x_3 \geq 50$
5. $3.37x_2 + 1.38x_3 \geq 38$
6. $4.49x_1 + 3.37x_2 + 1.38x_3 \geq 67$
7. $6x_1 - 6x_2 \geq 0$
8. $4x_1 - 5x_3 \geq 0$
9. $x_1, x_2, x_3$ are integers.

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'postage stamps'), ('x2', 'paper clips'), ('x3', 'headsets')],
'objective_function': '7.71*x1 + 6.19*x2 + 5.07*x3',
'constraints': [
    '4.49*x1 <= 233',
    '3.37*x2 <= 233',
    '1.38*x3 <= 233',
    '4.49*x1 + 1.38*x3 >= 50',
    '3.37*x2 + 1.38*x3 >= 38',
    '4.49*x1 + 3.37*x2 + 1.38*x3 >= 67',
    '6*x1 - 6*x2 >= 0',
    '4*x1 - 5*x3 >= 0',
    'x1, x2, x3 are integers'
]
}
```

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

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

    # Define the variables
    x1 = model.addVar(name="postage_stamps", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="paper_clips", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="headsets", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(7.71*x1 + 6.19*x2 + 5.07*x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(4.49*x1 <= 233)
    model.addConstr(3.37*x2 <= 233)
    model.addConstr(1.38*x3 <= 233)
    model.addConstr(4.49*x1 + 1.38*x3 >= 50)
    model.addConstr(3.37*x2 + 1.38*x3 >= 38)
    model.addConstr(4.49*x1 + 3.37*x2 + 1.38*x3 >= 67)
    model.addConstr(6*x1 - 6*x2 >= 0)
    model.addConstr(4*x1 - 5*x3 >= 0)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Postage stamps: {x1.varValue}")
        print(f"Paper clips: {x2.varValue}")
        print(f"Headsets: {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```