## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- 'x0' or 'hours worked by Laura'
- 'x1' or 'hours worked by Hank'
- 'x2' or 'hours worked by Peggy'
- 'x3' or 'hours worked by Mary'

## Step 2: Convert the problem into a symbolic representation
The symbolic representation of the variables is:
- x0: hours worked by Laura
- x1: hours worked by Hank
- x2: hours worked by Peggy
- x3: hours worked by Mary

## Step 3: Define the objective function in symbolic notation
The objective function to maximize is: 2*x0 + 4*x1 + 6*x2 + 9*x3

## Step 4: List all constraints in symbolic notation
Constraints:
- 17*x0 <= 426 
- 11*x1 <= 426 
- 13*x2 <= 426 
- 4*x3 <= 426 
- 8*x0 <= 175 
- 15*x1 <= 175 
- 12*x2 <= 175 
- 9*x3 <= 175 
- 13*x2 + 4*x3 >= 89 
- 17*x0 + 13*x2 + 4*x3 >= 66 
- 8*x0 + 15*x1 >= 41 
- 8*x0 + 12*x2 >= 33 
- 12*x2 + 9*x3 >= 34 
- 15*x1 + 12*x2 + 9*x3 >= 23 
- 8*x0 + 15*x1 + 9*x3 >= 23 
- 15*x1 + 12*x2 + 9*x3 >= 24 
- 8*x0 + 15*x1 + 9*x3 >= 24 
- 13*x2 + 4*x3 <= 392 
- 11*x1 + 4*x3 <= 369 
- 17*x0 + 11*x1 <= 235 
- 17*x0 + 11*x1 + 13*x2 + 4*x3 <= 235 
- 8*x0 + 12*x2 <= 119 
- 8*x0 + 15*x1 <= 48 
- 15*x1 + 9*x3 <= 152 
- 8*x0 + 9*x3 <= 151 
- 15*x1 + 12*x2 <= 127 
- 12*x2 + 9*x3 <= 148 
- 8*x0 + 15*x1 + 12*x2 <= 67 
- 8*x0 + 12*x2 + 9*x3 <= 172 
- 8*x0 + 15*x1 + 12*x2 + 9*x3 <= 172 

## 5: Consider variable bounds and types
- x0, x1, x3 are continuous
- x2 is integer

## 6: Write down the problem in JSON format
```json
{
    'sym_variables': [
        ['x0', 'hours worked by Laura'], 
        ['x1', 'hours worked by Hank'], 
        ['x2', 'hours worked by Peggy'], 
        ['x3', 'hours worked by Mary']
    ], 
    'objective_function': '2*x0 + 4*x1 + 6*x2 + 9*x3', 
    'constraints': [
        '17*x0 <= 426', '11*x1 <= 426', '13*x2 <= 426', '4*x3 <= 426',
        '8*x0 <= 175', '15*x1 <= 175', '12*x2 <= 175', '9*x3 <= 175',
        '13*x2 + 4*x3 >= 89', '17*x0 + 13*x2 + 4*x3 >= 66',
        '8*x0 + 15*x1 >= 41', '8*x0 + 12*x2 >= 33', '12*x2 + 9*x3 >= 34',
        '15*x1 + 12*x2 + 9*x3 >= 23', '8*x0 + 15*x1 + 9*x3 >= 23',
        '15*x1 + 12*x2 + 9*x3 >= 24', '8*x0 + 15*x1 + 9*x3 >= 24',
        '13*x2 + 4*x3 <= 392', '11*x1 + 4*x3 <= 369',
        '17*x0 + 11*x1 <= 235', '17*x0 + 11*x1 + 13*x2 + 4*x3 <= 235',
        '8*x0 + 12*x2 <= 119', '8*x0 + 15*x1 <= 48',
        '15*x1 + 9*x3 <= 152', '8*x0 + 9*x3 <= 151',
        '15*x1 + 12*x2 <= 127', '12*x2 + 9*x3 <= 148',
        '8*x0 + 15*x1 + 12*x2 <= 67', '8*x0 + 12*x2 + 9*x3 <= 172',
        '8*x0 + 15*x1 + 12*x2 + 9*x3 <= 172'
    ]
}
```

## 7: Implement the problem using Gurobi
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name='x0', lb=0, ub=None)  # hours worked by Laura
x1 = m.addVar(name='x1', lb=0, ub=None)  # hours worked by Hank
x2 = m.addVar(name='x2', lb=0, ub=None, vtype=gurobi.GRB.INTEGER)  # hours worked by Peggy
x3 = m.addVar(name='x3', lb=0, ub=None)  # hours worked by Mary

# Objective function
m.setObjective(2*x0 + 4*x1 + 6*x2 + 9*x3, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(17*x0 <= 426)
m.addConstr(11*x1 <= 426)
m.addConstr(13*x2 <= 426)
m.addConstr(4*x3 <= 426)

m.addConstr(8*x0 <= 175)
m.addConstr(15*x1 <= 175)
m.addConstr(12*x2 <= 175)
m.addConstr(9*x3 <= 175)

m.addConstr(13*x2 + 4*x3 >= 89)
m.addConstr(17*x0 + 13*x2 + 4*x3 >= 66)
m.addConstr(8*x0 + 15*x1 >= 41)
m.addConstr(8*x0 + 12*x2 >= 33)
m.addConstr(12*x2 + 9*x3 >= 34)
m.addConstr(15*x1 + 12*x2 + 9*x3 >= 23)
m.addConstr(8*x0 + 15*x1 + 9*x3 >= 23)
m.addConstr(15*x1 + 12*x2 + 9*x3 >= 24)
m.addConstr(8*x0 + 15*x1 + 9*x3 >= 24)

m.addConstr(13*x2 + 4*x3 <= 392)
m.addConstr(11*x1 + 4*x3 <= 369)
m.addConstr(17*x0 + 11*x1 <= 235)
m.addConstr(17*x0 + 11*x1 + 13*x2 + 4*x3 <= 235)

m.addConstr(8*x0 + 12*x2 <= 119)
m.addConstr(8*x0 + 15*x1 <= 48)
m.addConstr(15*x1 + 9*x3 <= 152)
m.addConstr(8*x0 + 9*x3 <= 151)
m.addConstr(15*x1 + 12*x2 <= 127)
m.addConstr(12*x2 + 9*x3 <= 148)
m.addConstr(8*x0 + 15*x1 + 12*x2 <= 67)
m.addConstr(8*x0 + 12*x2 + 9*x3 <= 172)
m.addConstr(8*x0 + 15*x1 + 12*x2 + 9*x3 <= 172)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.Status.OPTIMAL:
    print('Objective: ', m.objVal)
    print('Hours worked by Laura: ', x0.varValue)
    print('Hours worked by Hank: ', x1.varValue)
    print('Hours worked by Peggy: ', x2.varValue)
    print('Hours worked by Mary: ', x3.varValue)
else:
    print('No solution found')
```