To solve this problem, we first need to understand and translate the given natural language description into a symbolic representation that includes variables, an objective function, and constraints.

Let's denote:
- \(x_0\) as 'hours worked by Jean',
- \(x_1\) as 'hours worked by Laura',
- \(x_2\) as 'hours worked by Mary'.

The objective function is to maximize \(4x_0 + 5x_1 + 4x_2\).

Given constraints:
1. Work quality rating for Jean: \(19x_0\)
2. Dollar cost per hour for Jean: \(12x_0\)
3. Work quality rating for Laura: \(8x_1\)
4. Dollar cost per hour for Laura: \(14x_1\)
5. Work quality rating for Mary: \(16x_2\)
6. Dollar cost per hour for Mary: \(2x_2\)

Combined work quality ratings:
- For Jean and Mary: \(19x_0 + 16x_2 \geq 22\)
- For Jean and Laura: \(19x_0 + 8x_1 \geq 30\)
- For Laura and Mary: \(8x_1 + 16x_2 \geq 27\)
- For Jean and Laura: \(19x_0 + 8x_1 \leq 39\)
- For Laura and Mary: \(8x_1 + 16x_2 \leq 91\)
- For all three: \(19x_0 + 8x_1 + 16x_2 \leq 91\)

Combined dollar costs:
- For Jean and Mary: \(12x_0 + 2x_2 \leq 90\)
- For Jean and Laura: \(12x_0 + 14x_1 \leq 56\)
- For all three: \(12x_0 + 14x_1 + 2x_2 \leq 56\)

Symbolic representation:
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Jean'), 
        ('x1', 'hours worked by Laura'), 
        ('x2', 'hours worked by Mary')
    ], 
    'objective_function': '4*x0 + 5*x1 + 4*x2', 
    'constraints': [
        '19*x0 + 16*x2 >= 22',
        '19*x0 + 8*x1 >= 30',
        '8*x1 + 16*x2 >= 27',
        '19*x0 + 8*x1 <= 39',
        '8*x1 + 16*x2 <= 91',
        '19*x0 + 8*x1 + 16*x2 <= 91',
        '12*x0 + 2*x2 <= 90',
        '12*x0 + 14*x1 <= 56',
        '12*x0 + 14*x1 + 2*x2 <= 56'
    ]
}
```

Now, let's implement this in Gurobi Python:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Jean")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Laura")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Mary")

# Define objective function
m.setObjective(4*x0 + 5*x1 + 4*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(19*x0 + 16*x2 >= 22)
m.addConstr(19*x0 + 8*x1 >= 30)
m.addConstr(8*x1 + 16*x2 >= 27)
m.addConstr(19*x0 + 8*x1 <= 39)
m.addConstr(8*x1 + 16*x2 <= 91)
m.addConstr(19*x0 + 8*x1 + 16*x2 <= 91)
m.addConstr(12*x0 + 2*x2 <= 90)
m.addConstr(12*x0 + 14*x1 <= 56)
m.addConstr(12*x0 + 14*x1 + 2*x2 <= 56)

# Optimize model
m.optimize()

# Print solution
for v in m.getVars():
    print(f"{v.varName}: {v.x}")
print("Objective:", m.objVal)
```