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

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_0$ : hours worked by Bill
- $x_1$ : hours worked by George
- $x_2$ : hours worked by Laura

## 3: Define the objective function in symbolic notation
The objective function to maximize is $7.46x_0 + 6.91x_1 + 1.7x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $3x_0 \leq 78$ (Bill's paperwork competence rating)
- $4x_0 \leq 58$ (Bill's productivity rating)
- $8x_1 \leq 78$ (George's paperwork competence rating)
- $3x_1 \leq 58$ (George's productivity rating)
- $2x_2 \leq 78$ (Laura's paperwork competence rating)
- $3x_2 \leq 58$ (Laura's productivity rating)
- $3x_1 + 3x_2 \geq 17$ (total combined productivity rating from George and Laura)
- $-4x_1 + 10x_2 \geq 0$ ( constraint on George and Laura's hours)
- $3x_0 + 8x_1 \leq 36$ (total combined paperwork competence rating from Bill and George)
- $8x_1 + 2x_2 \leq 59$ (total combined paperwork competence rating from George and Laura)
- $3x_0 + 2x_2 \leq 73$ (total combined paperwork competence rating from Bill and Laura)
- $3x_0 + 8x_1 + 2x_2 \leq 73$ (total combined paperwork competence rating from all)
- $3x_1 + 3x_2 \leq 20$ (total combined productivity rating from George and Laura)
- $4x_0 + 3x_2 \leq 41$ (total combined productivity rating from Bill and Laura)
- $4x_0 + 3x_1 + 3x_2 \leq 41$ (total combined productivity rating from all)

## 5: Consider the variable bounds
- $x_0$ is a non-integer
- $x_1$ is an integer
- $x_2$ is a non-integer

## 6: Write down the problem in JSON format
```json
{
    'sym_variables': [('x0', 'hours worked by Bill'), ('x1', 'hours worked by George'), ('x2', 'hours worked by Laura')],
    'objective_function': '7.46*x0 + 6.91*x1 + 1.7*x2',
    'constraints': [
        '3*x0 <= 78',
        '4*x0 <= 58',
        '8*x1 <= 78',
        '3*x1 <= 58',
        '2*x2 <= 78',
        '3*x2 <= 58',
        '3*x1 + 3*x2 >= 17',
        '-4*x1 + 10*x2 >= 0',
        '3*x0 + 8*x1 <= 36',
        '8*x1 + 2*x2 <= 59',
        '3*x0 + 2*x2 <= 73',
        '3*x0 + 8*x1 + 2*x2 <= 73',
        '3*x1 + 3*x2 <= 20',
        '4*x0 + 3*x2 <= 41',
        '4*x0 + 3*x1 + 3*x2 <= 41'
    ]
}
```

## 7: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="x0", lb=0, ub=None)  # hours worked by Bill
    x1 = model.addVar(name="x1", lb=0, ub=None, vtype=gurobi.GRB.INTEGER)  # hours worked by George
    x2 = model.addVar(name="x2", lb=0, ub=None)  # hours worked by Laura

    # Define the objective function
    model.setObjective(7.46 * x0 + 6.91 * x1 + 1.7 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(3 * x0 <= 78)
    model.addConstr(4 * x0 <= 58)
    model.addConstr(8 * x1 <= 78)
    model.addConstr(3 * x1 <= 58)
    model.addConstr(2 * x2 <= 78)
    model.addConstr(3 * x2 <= 58)
    model.addConstr(3 * x1 + 3 * x2 >= 17)
    model.addConstr(-4 * x1 + 10 * x2 >= 0)
    model.addConstr(3 * x0 + 8 * x1 <= 36)
    model.addConstr(8 * x1 + 2 * x2 <= 59)
    model.addConstr(3 * x0 + 2 * x2 <= 73)
    model.addConstr(3 * x0 + 8 * x1 + 2 * x2 <= 73)
    model.addConstr(3 * x1 + 3 * x2 <= 20)
    model.addConstr(4 * x0 + 3 * x2 <= 41)
    model.addConstr(4 * x0 + 3 * x1 + 3 * x2 <= 41)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```