## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Mary', 'hours worked by Bill', and 'hours worked by Laura', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $2.25x_0 + 3.44x_1 + 1.13x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $12x_0 \leq 138$ (likelihood to quit index for Mary)
- $6x_0 \leq 155$ (work quality rating for Mary)
- $14x_0 \leq 153$ (dollar cost per hour for Mary)
- $19x_1 \leq 138$ (likelihood to quit index for Bill)
- $2x_1 \leq 155$ (work quality rating for Bill)
- $24x_1 \leq 153$ (dollar cost per hour for Bill)
- $25x_2 \leq 138$ (likelihood to quit index for Laura)
- $19x_2 \leq 155$ (work quality rating for Laura)
- $19x_2 \leq 153$ (dollar cost per hour for Laura)
- $19x_1 + 25x_2 \geq 41$ (combined likelihood to quit index for Bill and Laura)
- $12x_0 + 25x_2 \geq 36$ (combined likelihood to quit index for Mary and Laura)
- $2x_1 + 19x_2 \geq 39$ (combined work quality rating for Bill and Laura)
- $6x_0 + 19x_2 \geq 35$ (combined work quality rating for Mary and Laura)
- $6x_0 + 2x_1 + 19x_2 \geq 48$ (combined work quality rating for Mary, Bill, and Laura)
- $24x_1 + 19x_2 \geq 29$ (combined dollar cost per hour for Bill and Laura)
- $14x_0 + 24x_1 \geq 25$ (combined dollar cost per hour for Mary and Bill)
- $-6x_0 + 3x_1 \geq 0$ (relationship between hours worked by Mary and Bill)
- $12x_0 + 19x_1 \leq 133$ (combined likelihood to quit index for Mary and Bill)
- $12x_0 + 25x_2 \leq 71$ (combined likelihood to quit index for Mary and Laura)
- $12x_0 + 19x_1 + 25x_2 \leq 71$ (combined likelihood to quit index for Mary, Bill, and Laura)
- $6x_0 + 19x_2 \leq 101$ (combined work quality rating for Mary and Laura)
- $6x_0 + 2x_1 + 19x_2 \leq 101$ (combined work quality rating for Mary, Bill, and Laura)
- $24x_1 + 19x_2 \leq 73$ (combined dollar cost per hour for Bill and Laura)
- $14x_0 + 24x_1 \leq 96$ (combined dollar cost per hour for Mary and Bill)
- $14x_0 + 24x_1 + 19x_2 \leq 96$ (combined dollar cost per hour for Mary, Bill, and Laura)

## Step 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Mary'), 
        ('x1', 'hours worked by Bill'), 
        ('x2', 'hours worked by Laura')
    ], 
    'objective_function': '2.25*x0 + 3.44*x1 + 1.13*x2', 
    'constraints': [
        '12*x0 <= 138', '6*x0 <= 155', '14*x0 <= 153',
        '19*x1 <= 138', '2*x1 <= 155', '24*x1 <= 153',
        '25*x2 <= 138', '19*x2 <= 155', '19*x2 <= 153',
        '19*x1 + 25*x2 >= 41', '12*x0 + 25*x2 >= 36',
        '2*x1 + 19*x2 >= 39', '6*x0 + 19*x2 >= 35',
        '6*x0 + 2*x1 + 19*x2 >= 48', '24*x1 + 19*x2 >= 29',
        '14*x0 + 24*x1 >= 25', '-6*x0 + 3*x1 >= 0',
        '12*x0 + 19*x1 <= 133', '12*x0 + 25*x2 <= 71',
        '12*x0 + 19*x1 + 25*x2 <= 71', '6*x0 + 19*x2 <= 101',
        '6*x0 + 2*x1 + 19*x2 <= 101', '24*x1 + 19*x2 <= 73',
        '14*x0 + 24*x1 <= 96', '14*x0 + 24*x1 + 19*x2 <= 96'
    ]
}
```

## Step 5: Write the Gurobi code to solve the optimization problem
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Mary
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Bill
    x2 = model.addVar(name="x2", lb=0)  # hours worked by Laura

    # Define the objective function
    model.setObjective(2.25*x0 + 3.44*x1 + 1.13*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(12*x0 <= 138)
    model.addConstr(6*x0 <= 155)
    model.addConstr(14*x0 <= 153)
    model.addConstr(19*x1 <= 138)
    model.addConstr(2*x1 <= 155)
    model.addConstr(24*x1 <= 153)
    model.addConstr(25*x2 <= 138)
    model.addConstr(19*x2 <= 155)
    model.addConstr(19*x2 <= 153)
    model.addConstr(19*x1 + 25*x2 >= 41)
    model.addConstr(12*x0 + 25*x2 >= 36)
    model.addConstr(2*x1 + 19*x2 >= 39)
    model.addConstr(6*x0 + 19*x2 >= 35)
    model.addConstr(6*x0 + 2*x1 + 19*x2 >= 48)
    model.addConstr(24*x1 + 19*x2 >= 29)
    model.addConstr(14*x0 + 24*x1 >= 25)
    model.addConstr(-6*x0 + 3*x1 >= 0)
    model.addConstr(12*x0 + 19*x1 <= 133)
    model.addConstr(12*x0 + 25*x2 <= 71)
    model.addConstr(12*x0 + 19*x1 + 25*x2 <= 71)
    model.addConstr(6*x0 + 19*x2 <= 101)
    model.addConstr(6*x0 + 2*x1 + 19*x2 <= 101)
    model.addConstr(24*x1 + 19*x2 <= 73)
    model.addConstr(14*x0 + 24*x1 <= 96)
    model.addConstr(14*x0 + 24*x1 + 19*x2 <= 96)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Mary: ", x0.varValue)
        print("Hours worked by Bill: ", x1.varValue)
        print("Hours worked by Laura: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```