To solve the optimization problem described, we first need to convert the natural language description into a symbolic representation. The variables are 'hours worked by Bobby' and 'hours worked by Dale', which can be represented symbolically as $x_1$ and $x_2$, respectively.

The objective function is given as: minimize $2.71x_1 + 4.52x_2$.

The constraints based on the description are:

1. $2x_1 + 6x_2 \geq 13$ (total combined work quality rating from hours worked by Bobby and Dale should be 13 or more)
2. $2x_1 + 6x_2 \leq 25$ (total combined work quality rating from hours worked by Bobby plus hours worked by Dale should be 25 at maximum)
3. $7x_1 + 2x_2 \geq 9$ (total combined productivity rating from hours worked by Bobby and Dale should be greater than or equal to 9)
4. $7x_1 + 2x_2 \leq 20$ (total combined productivity rating from hours worked by Bobby and Dale must be 20 or less)
5. $-7x_1 + 5x_2 \geq 0$ (-7 times the number of hours worked by Bobby, plus 5 times the number of hours worked by Dale has to be no less than zero)

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'hours worked by Bobby'), ('x2', 'hours worked by Dale')],
    'objective_function': 'minimize 2.71*x1 + 4.52*x2',
    'constraints': [
        '2*x1 + 6*x2 >= 13',
        '2*x1 + 6*x2 <= 25',
        '7*x1 + 2*x2 >= 9',
        '7*x1 + 2*x2 <= 20',
        '-7*x1 + 5*x2 >= 0'
    ]
}
```

Now, let's write the Gurobi code to solve this problem:
```python
from gurobipy import *

# Create a model
m = Model("Optimization_Problem")

# Add variables
x1 = m.addVar(lb=0, name="hours_worked_by_Bobby")
x2 = m.addVar(lb=0, name="hours_worked_by_Dale")

# Set the objective function
m.setObjective(2.71*x1 + 4.52*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x1 + 6*x2 >= 13, "work_quality_rating_min")
m.addConstr(2*x1 + 6*x2 <= 25, "work_quality_rating_max")
m.addConstr(7*x1 + 2*x2 >= 9, "productivity_rating_min")
m.addConstr(7*x1 + 2*x2 <= 20, "productivity_rating_max")
m.addConstr(-7*x1 + 5*x2 >= 0, "additional_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Bobby: {x1.x}")
    print(f"Hours worked by Dale: {x2.x}")
else:
    print("No optimal solution found")
```