To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining the variables, the objective function, and the constraints using symbolic notation.

Let's denote:
- \(x_1\) as the hours worked by Jean,
- \(x_2\) as the hours worked by Laura,
- \(x_3\) as the hours worked by Mary.

The objective function is to maximize \(6x_1 + 2x_2 + 8x_3\).

The constraints are:
1. The total combined likelihood to quit index from hours worked by Jean and hours worked by Laura must be at least 141: \(1.81x_1 + 2.04x_2 \geq 141\).
2. The total combined likelihood to quit index from hours worked by Laura plus hours worked by Mary should be 327 or less: \(2.04x_2 + 2.11x_3 \leq 327\).
3. The total combined likelihood to quit index from hours worked by Jean and hours worked by Laura should be 321 at a maximum: \(1.81x_1 + 2.04x_2 \leq 321\).
4. The total combined likelihood to quit index from hours worked by Jean plus hours worked by Laura plus hours worked by Mary must be 321 at a maximum: \(1.81x_1 + 2.04x_2 + 2.11x_3 \leq 321\).

Given that all variables can be non-integer (float), we don't need to specify integer constraints.

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'hours worked by Jean'), ('x2', 'hours worked by Laura'), ('x3', 'hours worked by Mary')],
    'objective_function': '6*x1 + 2*x2 + 8*x3',
    'constraints': [
        '1.81*x1 + 2.04*x2 >= 141',
        '2.04*x2 + 2.11*x3 <= 327',
        '1.81*x1 + 2.04*x2 <= 321',
        '1.81*x1 + 2.04*x2 + 2.11*x3 <= 321'
    ]
}
```

Now, let's write the Gurobi code to solve this problem:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, name="hours_worked_by_Jean")
x2 = m.addVar(lb=0, name="hours_worked_by_Laura")
x3 = m.addVar(lb=0, name="hours_worked_by_Mary")

# Set the objective function
m.setObjective(6*x1 + 2*x2 + 8*x3, GRB.MAXIMIZE)

# Add constraints
m.addConstr(1.81*x1 + 2.04*x2 >= 141, "Minimum_combined_likelihood_Jean_Laura")
m.addConstr(2.04*x2 + 2.11*x3 <= 327, "Maximum_combined_likelihood_Laura_Mary")
m.addConstr(1.81*x1 + 2.04*x2 <= 321, "Maximum_combined_likelihood_Jean_Laura")
m.addConstr(1.81*x1 + 2.04*x2 + 2.11*x3 <= 321, "Maximum_total_combined_likelihood")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Jean: {x1.x}")
    print(f"Hours worked by Laura: {x2.x}")
    print(f"Hours worked by Mary: {x3.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```