## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Paul', 'hours worked by Bill', and 'hours worked by Dale', 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 Paul
- $x_1$ : hours worked by Bill
- $x_2$ : hours worked by Dale

## Step 3: Define the objective function in symbolic notation
The objective function to minimize is $9.56x_0 + 9.49x_1 + 9.3x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $17x_0 \leq 231$ (paperwork competence rating for Paul)
- $7x_0 \leq 200$ (work quality rating for Paul)
- $18x_1 \leq 231$ (paperwork competence rating for Bill)
- $8x_1 \leq 200$ (work quality rating for Bill)
- $12x_2 \leq 231$ (paperwork competence rating for Dale)
- $3x_2 \leq 200$ (work quality rating for Dale)
- $18x_1 + 12x_2 \geq 35$ (combined paperwork competence rating for Bill and Dale)
- $17x_0 + 12x_2 \geq 77$ (combined paperwork competence rating for Paul and Dale)
- $17x_0 + 18x_1 + 12x_2 \geq 77$ (combined paperwork competence rating for all)
- $7x_0 + 8x_1 \geq 38$ (combined work quality rating for Paul and Bill)
- $7x_0 + 8x_1 + 3x_2 \geq 63$ (combined work quality rating for all)
- $x_0 - 4x_2 \geq 0$ (constraint involving Paul and Dale)
- $5x_1 - 8x_2 \geq 0$ (constraint involving Bill and Dale)

## 5: Create a JSON object representing the problem symbolically
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Paul'), 
        ('x1', 'hours worked by Bill'), 
        ('x2', 'hours worked by Dale')
    ], 
    'objective_function': '9.56*x0 + 9.49*x1 + 9.3*x2', 
    'constraints': [
        '17*x0 <= 231',
        '7*x0 <= 200',
        '18*x1 <= 231',
        '8*x1 <= 200',
        '12*x2 <= 231',
        '3*x2 <= 200',
        '18*x1 + 12*x2 >= 35',
        '17*x0 + 12*x2 >= 77',
        '17*x0 + 18*x1 + 12*x2 >= 77',
        '7*x0 + 8*x1 >= 38',
        '7*x0 + 8*x1 + 3*x2 >= 63',
        'x0 - 4*x2 >= 0',
        '5*x1 - 8*x2 >= 0'
    ]
}
```

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

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

    # Define the variables
    x0 = model.addVar(name='hours_worked_by_Paul', lb=0)
    x1 = model.addVar(name='hours_worked_by_Bill', lb=0)
    x2 = model.addVar(name='hours_worked_by_Dale', lb=0)

    # Define the objective function
    model.setObjective(9.56 * x0 + 9.49 * x1 + 9.3 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(17 * x0 <= 231)
    model.addConstr(7 * x0 <= 200)
    model.addConstr(18 * x1 <= 231)
    model.addConstr(8 * x1 <= 200)
    model.addConstr(12 * x2 <= 231)
    model.addConstr(3 * x2 <= 200)
    model.addConstr(18 * x1 + 12 * x2 >= 35)
    model.addConstr(17 * x0 + 12 * x2 >= 77)
    model.addConstr(17 * x0 + 18 * x1 + 12 * x2 >= 77)
    model.addConstr(7 * x0 + 8 * x1 >= 38)
    model.addConstr(7 * x0 + 8 * x1 + 3 * x2 >= 63)
    model.addConstr(x0 - 4 * x2 >= 0)
    model.addConstr(5 * x1 - 8 * x2 >= 0)

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```