## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Mary' and 'hours worked by Bobby', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $6.47x_1 + 9.14x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
1. $7x_1 \geq 7x_1$ (Mary's paperwork competence rating is 7, but this is inherently satisfied as it's an equality and not a constraint on $x_1$ directly in a meaningful way; however, we note $x_1$ must be an integer),
2. $1x_2 \geq 1x_2$ (Bobby's paperwork competence rating is 1, similar to Mary's, this is not a constraint),
3. $7x_1 + 1x_2 \geq 30$,
4. $8x_1 - 5x_2 \geq 0$,
5. $7x_1 + 1x_2 \leq 71$.

## 4: Correctly interpret and list all constraints
- $7x_1 = 7$ (from Mary's rating, implying $x_1 = 1$),
- $x_2$ is continuous,
- $7x_1 + x_2 \geq 30$,
- $8x_1 - 5x_2 \geq 0$,
- $7x_1 + x_2 \leq 71$.

## 5: Convert the problem into a Gurobi model
We will use Gurobi to solve this optimization problem.

## 6: Write down the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'hours worked by Mary'), ('x2', 'hours worked by Bobby')],
    'objective_function': '6.47*x1 + 9.14*x2',
    'constraints': [
        'x1 >= 0', 
        'x2 >= 0', 
        '7*x1 + x2 >= 30', 
        '8*x1 - 5*x2 >= 0', 
        '7*x1 + x2 <= 71', 
        'x1 % 1 == 0' # integer constraint for x1
    ]
}
```

## 7: Implement the problem in Gurobi
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="hours_worked_by_Mary", vtype=gurobi.GRB.INTEGER) # integer hours for Mary
    x2 = model.addVar(name="hours_worked_by_Bobby") # continuous hours for Bobby

    # Objective function
    model.setObjective(6.47 * x1 + 9.14 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(7 * x1 + x2 >= 30)
    model.addConstr(8 * x1 - 5 * x2 >= 0)
    model.addConstr(7 * x1 + x2 <= 71)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Mary: {x1.varValue}")
        print(f"Hours worked by Bobby: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```