To convert the given natural language description of an optimization problem into a symbolic representation and then solve it using Gurobi, we first need to identify the variables, objective function, and constraints.

The variables are:
- Hours worked by George (let's denote this as `x1`)
- Hours worked by Bill (denoted as `x2`)

The objective function is to maximize: `1.69*x1 + 5.4*x2`

Constraints:
1. Total combined productivity rating >= 63: `14*x1 + 2*x2 >= 63`
2. Total combined likelihood to quit index >= 31: `1*x1 + 12*x2 >= 31`
3. Total combined organization score >= 24: `4*x1 + 13*x2 >= 24`
4. Total combined computer competence rating >= 56: `6*x1 + 13*x2 >= 56`
5. `-6*x1 + 9*x2 >= 0`
6. Total combined productivity rating <= 77: `14*x1 + 2*x2 <= 77`
7. Total combined likelihood to quit index <= 65: `1*x1 + 12*x2 <= 65`
8. Total combined organization score <= 37: `4*x1 + 13*x2 <= 37`
9. Total combined computer competence rating <= 115: `6*x1 + 13*x2 <= 115`
10. `x1` and `x2` must be whole numbers (integer constraints).

Given the symbolic representation, we can now formulate this problem in Gurobi.

```json
{
  'sym_variables': [('x1', 'hours worked by George'), ('x2', 'hours worked by Bill')],
  'objective_function': 'Maximize 1.69*x1 + 5.4*x2',
  'constraints': [
    '14*x1 + 2*x2 >= 63',
    '1*x1 + 12*x2 >= 31',
    '4*x1 + 13*x2 >= 24',
    '6*x1 + 13*x2 >= 56',
    '-6*x1 + 9*x2 >= 0',
    '14*x1 + 2*x2 <= 77',
    '1*x1 + 12*x2 <= 65',
    '4*x1 + 13*x2 <= 37',
    '6*x1 + 13*x2 <= 115'
  ]
}
```

Now, let's implement this optimization problem in Gurobi using Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_George")
x2 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Bill")

# Set the objective function
m.setObjective(1.69*x1 + 5.4*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(14*x1 + 2*x2 >= 63, "productivity_rating")
m.addConstr(1*x1 + 12*x2 >= 31, "likelihood_to_quit_index_min")
m.addConstr(4*x1 + 13*x2 >= 24, "organization_score_min")
m.addConstr(6*x1 + 13*x2 >= 56, "computer_competence_rating_min")
m.addConstr(-6*x1 + 9*x2 >= 0, "mixed_constraint")
m.addConstr(14*x1 + 2*x2 <= 77, "productivity_rating_max")
m.addConstr(1*x1 + 12*x2 <= 65, "likelihood_to_quit_index_max")
m.addConstr(4*x1 + 13*x2 <= 37, "organization_score_max")
m.addConstr(6*x1 + 13*x2 <= 115, "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 George: {x1.x}")
    print(f"Hours worked by Bill: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```