To solve this optimization problem, we first need to understand and translate the given description into a symbolic representation. The variables are 'hours worked by Laura' and 'hours worked by Bill'. We'll denote these as `x1` and `x2`, respectively.

The objective function is to minimize `9*x1 + 8*x2`.

Given the constraints:
- `11*x1 + 3*x2 >= 34` (total combined likelihood to quit index)
- `13*x1 + 4*x2 >= 13` (total combined dollar cost per hour)
- `10*x1 + 14*x2 >= 36` (total combined productivity rating)
- `7*x1 + 17*x2 >= 39` (total combined computer competence rating)
- `-3*x1 + x2 >= 0`
- `11*x1 + 3*x2 <= 52` (upper bound on likelihood to quit index)
- `13*x1 + 4*x2 <= 38` (upper bound on dollar cost per hour)
- `10*x1 + 14*x2 <= 59` (upper bound on productivity rating)
- `7*x1 + 17*x2 <= 77` (upper bound on computer competence rating)

We allow `x1` to be fractional but require `x2` to be an integer.

Symbolic representation:
```json
{
    'sym_variables': [('x1', 'hours worked by Laura'), ('x2', 'hours worked by Bill')],
    'objective_function': '9*x1 + 8*x2',
    'constraints': [
        '11*x1 + 3*x2 >= 34',
        '13*x1 + 4*x2 >= 13',
        '10*x1 + 14*x2 >= 36',
        '7*x1 + 17*x2 >= 39',
        '-3*x1 + x2 >= 0',
        '11*x1 + 3*x2 <= 52',
        '13*x1 + 4*x2 <= 38',
        '10*x1 + 14*x2 <= 59',
        '7*x1 + 17*x2 <= 77'
    ]
}
```

Now, let's implement this problem using Gurobi in Python:
```python
from gurobipy import *

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

# Add variables to the model
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Laura")
x2 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Bill")

# Set the objective function
m.setObjective(9*x1 + 8*x2, GRB.MINIMIZE)

# Add constraints to the model
m.addConstr(11*x1 + 3*x2 >= 34, "likelihood_to_quit_index_min")
m.addConstr(13*x1 + 4*x2 >= 13, "dollar_cost_per_hour_min")
m.addConstr(10*x1 + 14*x2 >= 36, "productivity_rating_min")
m.addConstr(7*x1 + 17*x2 >= 39, "computer_competence_rating_min")
m.addConstr(-3*x1 + x2 >= 0, "other_constraint")
m.addConstr(11*x1 + 3*x2 <= 52, "likelihood_to_quit_index_max")
m.addConstr(13*x1 + 4*x2 <= 38, "dollar_cost_per_hour_max")
m.addConstr(10*x1 + 14*x2 <= 59, "productivity_rating_max")
m.addConstr(7*x1 + 17*x2 <= 77, "computer_competence_rating_max")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Laura: {x1.x}")
    print(f"Hours worked by Bill: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```