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

## Step 2: Define the symbolic representation of the problem
The objective function to minimize is $9x_0 + 3x_1 + x_2$.

## Step 3: List the constraints
The constraints given are:
- $6x_0 \geq 6 \cdot 6$ is not correct, it is just $x_0$ has a productivity rating of 6, which is a fixed value, not a constraint in the traditional sense but a given attribute.
- $8x_0$ is not a constraint, $x_0$ has a work quality rating of 8.
- $11x_0$ is not a constraint, $x_0$ has an organization score of 11.
- Similarly, $x_1$ and $x_2$ have fixed ratings.

## 4: Translate given attributes into constraints where applicable
Given attributes:
- Productivity rating: $r0 = 6x_0 + 7x_1 + 19x_2$
- Work quality rating: $r1 = 8x_0 + 15x_1 + 22x_2$
- Organization score: $r2 = 11x_0 + 14x_1 + 15x_2$

## 5: Express problem constraints using symbolic variables
Constraints:
1. $6x_0 + 7x_1 \geq 64$
2. $6x_0 + 19x_2 \geq 37$
3. $6x_0 + 7x_1 + 19x_2 \geq 71$
4. $8x_1 + 22x_2 \geq 50$
5. $8x_0 + 15x_1 \geq 59$
6. $8x_0 + 22x_2 \geq 40$
7. $8x_0 + 15x_1 + 22x_2 \geq 40$
8. $14x_1 + 15x_2 \geq 53$
9. $11x_0 + 14x_1 + 15x_2 \geq 53$
10. $-8x_0 + 4x_2 \geq 0$
11. $7x_1 + 19x_2 \leq 166$

## 6: Consider variable bounds and types
- $x_0$ is an integer
- $x_1$ is an integer
- $x_2$ is a continuous variable

## 7: Formulate the problem in Gurobi
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define variables
x0 = m.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # hours worked by Ringo
x1 = m.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # hours worked by John
x2 = m.addVar(name="x2")  # hours worked by Bill

# Objective function
m.setObjective(9 * x0 + 3 * x1 + x2, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(6 * x0 + 7 * x1 >= 64)
m.addConstr(6 * x0 + 19 * x2 >= 37)
m.addConstr(6 * x0 + 7 * x1 + 19 * x2 >= 71)
m.addConstr(8 * x1 + 22 * x2 >= 50)
m.addConstr(8 * x0 + 15 * x1 >= 59)
m.addConstr(8 * x0 + 22 * x2 >= 40)
m.addConstr(8 * x0 + 15 * x1 + 22 * x2 >= 40)
m.addConstr(14 * x1 + 15 * x2 >= 53)
m.addConstr(11 * x0 + 14 * x1 + 15 * x2 >= 53)
m.addConstr(-8 * x0 + 4 * x2 >= 0)
m.addConstr(7 * x1 + 19 * x2 <= 166)

# Optimize
m.optimize()

# Print solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
else:
    print("No solution found")
```

## 8: Symbolic representation
```json
{
    "sym_variables": [
        ["x0", "hours worked by Ringo"],
        ["x1", "hours worked by John"],
        ["x2", "hours worked by Bill"]
    ],
    "objective_function": "9*x0 + 3*x1 + x2",
    "constraints": [
        "6*x0 + 7*x1 >= 64",
        "6*x0 + 19*x2 >= 37",
        "6*x0 + 7*x1 + 19*x2 >= 71",
        "8*x1 + 22*x2 >= 50",
        "8*x0 + 15*x1 >= 59",
        "8*x0 + 22*x2 >= 40",
        "8*x0 + 15*x1 + 22*x2 >= 40",
        "14*x1 + 15*x2 >= 53",
        "11*x0 + 14*x1 + 15*x2 >= 53",
        "-8*x0 + 4*x2 >= 0",
        "7*x1 + 19*x2 <= 166"
    ]
}
```