## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Bobby', 'hours worked by Laura', and 'hours worked by Bill', 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 minimize is $8x_0 + 8x_1 + 4x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $10x_0 = 10$
- $5x_0 = 5$
- $3x_1 = 3$
- $7x_1 = 7$
- $2x_2 = 2$
- $11x_2 = 11$
- $10x_0 + 2x_2 \geq 19$
- $10x_0 + 3x_1 \geq 7$
- $10x_0 + 3x_1 + 2x_2 \geq 7$
- $7x_1 + 11x_2 \geq 20$
- $5x_0 + 11x_2 \geq 21$
- $5x_0 + 7x_1 + 11x_2 \geq 21$
- $-3x_0 + 9x_1 \geq 0$
- $3x_1 + 2x_2 \leq 61$

## 4: Convert the problem into a Gurobi model
We will use Gurobi to solve this optimization problem.

## 5: Write the Gurobi code
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name="hours_worked_by_Bobby", lb=0)
x1 = m.addVar(name="hours_worked_by_Laura", lb=0)
x2 = m.addVar(name="hours_worked_by_Bill", lb=0)

# Objective function
m.setObjective(8*x0 + 8*x1 + 4*x2, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(10*x0 == 10, name="Bobby_organization_score")
m.addConstr(5*x0 == 5, name="Bobby_work_quality_rating")
m.addConstr(3*x1 == 3, name="Laura_organization_score")
m.addConstr(7*x1 == 7, name="Laura_work_quality_rating")
m.addConstr(2*x2 == 2, name="Bill_organization_score")
m.addConstr(11*x2 == 11, name="Bill_work_quality_rating")
m.addConstr(10*x0 + 2*x2 >= 19, name="combined_organization_score_Bobby_Bill")
m.addConstr(10*x0 + 3*x1 >= 7, name="combined_organization_score_Bobby_Laura")
m.addConstr(10*x0 + 3*x1 + 2*x2 >= 7, name="combined_organization_score_all")
m.addConstr(7*x1 + 11*x2 >= 20, name="combined_work_quality_rating_Laura_Bill")
m.addConstr(5*x0 + 11*x2 >= 21, name="combined_work_quality_rating_Bobby_Bill")
m.addConstr(5*x0 + 7*x1 + 11*x2 >= 21, name="combined_work_quality_rating_all")
m.addConstr(-3*x0 + 9*x1 >= 0, name="Bobby_Laura_constraint")
m.addConstr(3*x1 + 2*x2 <= 61, name="Laura_Bill_organization_score")

# Optimize the model
m.optimize()

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

## 6: Symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'hours worked by Bobby'), ('x1', 'hours worked by Laura'), ('x2', 'hours worked by Bill')],
    'objective_function': '8*x0 + 8*x1 + 4*x2',
    'constraints': [
        '10*x0 = 10',
        '5*x0 = 5',
        '3*x1 = 3',
        '7*x1 = 7',
        '2*x2 = 2',
        '11*x2 = 11',
        '10*x0 + 2*x2 >= 19',
        '10*x0 + 3*x1 >= 7',
        '10*x0 + 3*x1 + 2*x2 >= 7',
        '7*x1 + 11*x2 >= 20',
        '5*x0 + 11*x2 >= 21',
        '5*x0 + 7*x1 + 11*x2 >= 21',
        '-3*x0 + 9*x1 >= 0',
        '3*x1 + 2*x2 <= 61'
    ]
}
```