To tackle this problem, let's first break down the natural language description into a symbolic representation that we can work with. We have two variables:

- Hours worked by Bill: $x_1$
- Hours worked by Bobby: $x_2$

The objective function to minimize is described as $4.11x_1 + 4.49x_2$.

Now, let's list out the constraints based on the description provided:

1. The total combined dollar cost per hour from hours worked by Bill plus hours worked by Bobby must be at least 38: $4x_1 + 9x_2 \geq 38$
2. The constraint that the total should be exactly 38 is not applicable as it contradicts with having a minimum or more, so we consider only $\geq$ for this case.
3. The total combined likelihood to quit index from hours worked by Bill plus hours worked by Bobby has to be at least 46: $x_1 + 3x_2 \geq 46$
4. Again, considering the exact requirement is not feasible with "at least," we focus on $\geq$.
5. The condition that minus two times the number of hours worked by Bill, plus two times the number of hours worked by Bobby should be at least zero translates to: $-2x_1 + 2x_2 \geq 0$
6. The total combined dollar cost per hour from hours worked by Bill plus hours worked by Bobby has to be 87 or less: $4x_1 + 9x_2 \leq 87$
7. The total combined likelihood to quit index from hours worked by Bill plus hours worked by Bobby should be less than or equal to 94: $x_1 + 3x_2 \leq 94$

Given that we can use non-integer amounts of hours worked for both, all variables are continuous.

Thus, our symbolic representation is:
```json
{
    'sym_variables': [('x1', 'hours worked by Bill'), ('x2', 'hours worked by Bobby')],
    'objective_function': '4.11*x1 + 4.49*x2',
    'constraints': [
        '4*x1 + 9*x2 >= 38',
        'x1 + 3*x2 >= 46',
        '-2*x1 + 2*x2 >= 0',
        '4*x1 + 9*x2 <= 87',
        'x1 + 3*x2 <= 94'
    ]
}
```

Now, let's implement this in Gurobi Python code:

```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_Bill")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Bobby")

# Set the objective function
m.setObjective(4.11*x1 + 4.49*x2, GRB.MINIMIZE)

# Add constraints to the model
m.addConstr(4*x1 + 9*x2 >= 38, "dollar_cost_min")
m.addConstr(x1 + 3*x2 >= 46, "quit_index_min")
m.addConstr(-2*x1 + 2*x2 >= 0, "hours_balance")
m.addConstr(4*x1 + 9*x2 <= 87, "dollar_cost_max")
m.addConstr(x1 + 3*x2 <= 94, "quit_index_max")

# Optimize the model
m.optimize()

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