## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Dale', 'hours worked by Peggy', 'hours worked by Bill', and 'hours worked by Ringo', which can be represented symbolically as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $3x_0 + 9x_1 + 2x_2 + 2x_3$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $6x_0 \leq 264$ (work quality rating for Dale)
- $13x_0 \leq 237$ (productivity rating for Dale)
- $6x_1 \leq 264$ (work quality rating for Peggy)
- $9x_1 \leq 237$ (productivity rating for Peggy)
- $21x_2 \leq 264$ (work quality rating for Bill)
- $8x_2 \leq 237$ (productivity rating for Bill)
- $18x_3 \leq 264$ (work quality rating for Ringo)
- $12x_3 \leq 237$ (productivity rating for Ringo)
- $6x_1 + 18x_3 \geq 36$ (combined work quality rating for Peggy and Ringo)
- $6x_0 + 21x_2 \geq 33$ (combined work quality rating for Dale and Bill)
- $6x_1 + 21x_2 \geq 62$ (combined work quality rating for Peggy and Bill)
- $21x_2 + 18x_3 \geq 60$ (combined work quality rating for Bill and Ringo)
- $6x_0 + 6x_1 + 21x_2 \geq 53$ (combined work quality rating for Dale, Peggy, and Bill)
- $6x_0 + 21x_2 + 18x_3 \geq 53$ (combined work quality rating for Dale, Bill, and Ringo)
- $6x_0 + 6x_1 + 21x_2 \geq 42$ (combined work quality rating for Dale, Peggy, and Bill)
- $6x_0 + 21x_2 + 18x_3 \geq 42$ (combined work quality rating for Dale, Bill, and Ringo)
- $9x_1 + 8x_2 \geq 24$ (combined productivity rating for Peggy and Bill)
- $13x_0 + 12x_3 \geq 33$ (combined productivity rating for Dale and Ringo)
- $9x_1 + 12x_3 \geq 48$ (combined productivity rating for Peggy and Ringo)
- $13x_0 + 8x_2 \geq 31$ (combined productivity rating for Dale and Bill)
- $8x_2 + 12x_3 \geq 27$ (combined productivity rating for Bill and Ringo)
- $6x_0 + 18x_3 \leq 185$ (combined work quality rating for Dale and Ringo)
- $21x_2 + 18x_3 \leq 217$ (combined work quality rating for Bill and Ringo)
- $6x_1 + 21x_2 \leq 95$ (combined work quality rating for Peggy and Bill)
- $6x_0 + 6x_1 + 21x_2 + 18x_3 \leq 95$ (combined work quality rating for all)
- $13x_0 + 8x_2 \leq 237$ (combined productivity rating for Dale and Bill)
- $8x_2 + 12x_3 \leq 145$ (combined productivity rating for Bill and Ringo)
- $13x_0 + 12x_3 \leq 128$ (combined productivity rating for Dale and Ringo)
- $13x_0 + 9x_1 + 8x_2 + 12x_3 \leq 128$ (combined productivity rating for all)

## 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Dale'),
        ('x1', 'hours worked by Peggy'),
        ('x2', 'hours worked by Bill'),
        ('x3', 'hours worked by Ringo')
    ],
    'objective_function': '3*x0 + 9*x1 + 2*x2 + 2*x3',
    'constraints': [
        '6*x0 <= 264',
        '13*x0 <= 237',
        '6*x1 <= 264',
        '9*x1 <= 237',
        '21*x2 <= 264',
        '8*x2 <= 237',
        '18*x3 <= 264',
        '12*x3 <= 237',
        '6*x1 + 18*x3 >= 36',
        '6*x0 + 21*x2 >= 33',
        '6*x1 + 21*x2 >= 62',
        '21*x2 + 18*x3 >= 60',
        '6*x0 + 6*x1 + 21*x2 >= 53',
        '6*x0 + 21*x2 + 18*x3 >= 53',
        '6*x0 + 6*x1 + 21*x2 >= 42',
        '6*x0 + 21*x2 + 18*x3 >= 42',
        '9*x1 + 8*x2 >= 24',
        '13*x0 + 12*x3 >= 33',
        '9*x1 + 12*x3 >= 48',
        '13*x0 + 8*x2 >= 31',
        '8*x2 + 12*x3 >= 27',
        '6*x0 + 18*x3 <= 185',
        '21*x2 + 18*x3 <= 217',
        '6*x1 + 21*x2 <= 95',
        '6*x0 + 6*x1 + 21*x2 + 18*x3 <= 95',
        '13*x0 + 8*x2 <= 237',
        '8*x2 + 12*x3 <= 145',
        '13*x0 + 12*x3 <= 128',
        '13*x0 + 9*x1 + 8*x2 + 12*x3 <= 128'
    ]
}
```

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

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Dale
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Peggy
    x2 = model.addVar(name="x2", lb=0)  # hours worked by Bill
    x3 = model.addVar(name="x3", lb=0)  # hours worked by Ringo

    # Objective function
    model.setObjective(3*x0 + 9*x1 + 2*x2 + 2*x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(6*x0 <= 264)
    model.addConstr(13*x0 <= 237)
    model.addConstr(6*x1 <= 264)
    model.addConstr(9*x1 <= 237)
    model.addConstr(21*x2 <= 264)
    model.addConstr(8*x2 <= 237)
    model.addConstr(18*x3 <= 264)
    model.addConstr(12*x3 <= 237)
    model.addConstr(6*x1 + 18*x3 >= 36)
    model.addConstr(6*x0 + 21*x2 >= 33)
    model.addConstr(6*x1 + 21*x2 >= 62)
    model.addConstr(21*x2 + 18*x3 >= 60)
    model.addConstr(6*x0 + 6*x1 + 21*x2 >= 53)
    model.addConstr(6*x0 + 21*x2 + 18*x3 >= 53)
    model.addConstr(6*x0 + 6*x1 + 21*x2 >= 42)
    model.addConstr(6*x0 + 21*x2 + 18*x3 >= 42)
    model.addConstr(9*x1 + 8*x2 >= 24)
    model.addConstr(13*x0 + 12*x3 >= 33)
    model.addConstr(9*x1 + 12*x3 >= 48)
    model.addConstr(13*x0 + 8*x2 >= 31)
    model.addConstr(8*x2 + 12*x3 >= 27)
    model.addConstr(6*x0 + 18*x3 <= 185)
    model.addConstr(21*x2 + 18*x3 <= 217)
    model.addConstr(6*x1 + 21*x2 <= 95)
    model.addConstr(6*x0 + 6*x1 + 21*x2 + 18*x3 <= 95)
    model.addConstr(13*x0 + 8*x2 <= 237)
    model.addConstr(8*x2 + 12*x3 <= 145)
    model.addConstr(13*x0 + 12*x3 <= 128)
    model.addConstr(13*x0 + 9*x1 + 8*x2 + 12*x3 <= 128)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Dale: ", x0.varValue)
        print("Hours worked by Peggy: ", x1.varValue)
        print("Hours worked by Bill: ", x2.varValue)
        print("Hours worked by Ringo: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```