## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Dale', 'hours worked by Peggy', 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 $1 \cdot x_0 + 3 \cdot x_1 + 6 \cdot x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $12x_1 + 11x_2 \geq 24$
- $20x_0 + 12x_1 \geq 36$
- $20x_0 + 12x_1 + 11x_2 \geq 36$
- $13x_0 + 18x_2 \geq 15$
- $15x_1 + 18x_2 \geq 33$
- $13x_0 + 15x_1 + 18x_2 \geq 23$
- $10x_1 + 15x_2 \geq 32$
- $20x_0 + 10x_1 \geq 23$
- $20x_0 + 10x_1 + 15x_2 \geq 24$
- $-10x_1 + 10x_2 \geq 0$
- $13x_0 + 15x_1 \leq 103$
- $13x_0 + 18x_2 \leq 66$
- $13x_0 + 15x_1 + 18x_2 \leq 115$
- $10x_1 + 15x_2 \leq 95$
- $20x_0 + 15x_2 \leq 42$

## Step 4: Provide the symbolic representation of the problem
```json
{
'sym_variables': [
    ('x0', 'hours worked by Dale'),
    ('x1', 'hours worked by Peggy'),
    ('x2', 'hours worked by Bill')
],
'objective_function': '1*x0 + 3*x1 + 6*x2',
'constraints': [
    '12*x1 + 11*x2 >= 24',
    '20*x0 + 12*x1 >= 36',
    '20*x0 + 12*x1 + 11*x2 >= 36',
    '13*x0 + 18*x2 >= 15',
    '15*x1 + 18*x2 >= 33',
    '13*x0 + 15*x1 + 18*x2 >= 23',
    '10*x1 + 15*x2 >= 32',
    '20*x0 + 10*x1 >= 23',
    '20*x0 + 10*x1 + 15*x2 >= 24',
    '-10*x1 + 10*x2 >= 0',
    '13*x0 + 15*x1 <= 103',
    '13*x0 + 18*x2 <= 66',
    '13*x0 + 15*x1 + 18*x2 <= 115',
    '10*x1 + 15*x2 <= 95',
    '20*x0 + 15*x2 <= 42'
]
}
```

## Step 5: Write the Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the 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

    # Define the objective function
    model.setObjective(x0 + 3 * x1 + 6 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(12 * x1 + 11 * x2 >= 24)
    model.addConstr(20 * x0 + 12 * x1 >= 36)
    model.addConstr(20 * x0 + 12 * x1 + 11 * x2 >= 36)
    model.addConstr(13 * x0 + 18 * x2 >= 15)
    model.addConstr(15 * x1 + 18 * x2 >= 33)
    model.addConstr(13 * x0 + 15 * x1 + 18 * x2 >= 23)
    model.addConstr(10 * x1 + 15 * x2 >= 32)
    model.addConstr(20 * x0 + 10 * x1 >= 23)
    model.addConstr(20 * x0 + 10 * x1 + 15 * x2 >= 24)
    model.addConstr(-10 * x1 + 10 * x2 >= 0)
    model.addConstr(13 * x0 + 15 * x1 <= 103)
    model.addConstr(13 * x0 + 18 * x2 <= 66)
    model.addConstr(13 * x0 + 15 * x1 + 18 * x2 <= 115)
    model.addConstr(10 * x1 + 15 * x2 <= 95)
    model.addConstr(20 * x0 + 15 * x2 <= 42)

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```