## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Bill', 'hours worked by Dale', 'hours worked by Jean', and 'hours worked by Mary', 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 minimize is $9x_0 + 7x_1 + 1x_2 + 5x_3$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $4x_0 \leq 139$
- $4x_0 \leq 189$
- $6x_0 \leq 179$
- $15x_0 \leq 330$
- $6x_1 \leq 139$
- $14x_1 \leq 189$
- $2x_1 \leq 179$
- $3x_1 \leq 330$
- $19x_2 \leq 139$
- $19x_2 \leq 189$
- $2x_2 \leq 179$
- $20x_2 \leq 330$
- $17x_3 \leq 139$
- $8x_3 \leq 189$
- $3x_3 \leq 179$
- $9x_3 \leq 330$
- $6x_1 + 17x_3 \geq 26$
- $4x_0 + 19x_2 \geq 11$
- $6x_1 + 19x_2 \geq 18$
- $4x_0 + 6x_1 + 19x_2 + 17x_3 \geq 18$
- $4x_0 + 19x_2 \geq 36$
- $14x_1 + 19x_2 \geq 19$
- $4x_0 + 14x_1 + 19x_2 + 8x_3 \geq 19$
- $6x_0 + 3x_3 \geq 17$
- $2x_2 + 3x_3 \geq 42$
- $6x_0 + 2x_1 \geq 19$
- $6x_0 + 2x_2 \geq 35$
- $2x_1 + 2x_2 \geq 38$
- $2x_1 + 3x_3 \geq 38$
- $6x_0 + 2x_1 + 2x_2 + 3x_3 \geq 38$
- $15x_0 + 3x_1 \geq 58$
- $15x_0 + 9x_3 \geq 63$
- $20x_2 + 9x_3 \geq 74$
- $3x_1 + 20x_2 \geq 45$
- $3x_1 + 9x_3 \geq 63$
- $15x_0 + 20x_2 + 9x_3 \geq 74$
- $15x_0 + 3x_1 + 20x_2 + 9x_3 \geq 74$
- $-3x_0 + x_1 \geq 0$
- $6x_1 + 19x_2 \leq 113$
- $4x_0 + 19x_2 \leq 116$
- $6x_1 + 17x_3 \leq 122$
- $19x_2 + 17x_3 \leq 85$
- $4x_0 + 6x_1 \leq 101$
- $4x_0 + 19x_2 \leq 65$
- $4x_0 + 19x_2 + 17x_3 \leq 63$
- $4x_0 + 19x_2 \leq 104$
- $14x_1 + 19x_2 \leq 88$
- $4x_0 + 19x_2 + 8x_3 \leq 171$
- $4x_0 + 14x_1 + 19x_2 \leq 117$
- $14x_1 + 19x_2 + 8x_3 \leq 72$
- $2x_1 + 2x_2 \leq 147$
- $6x_0 + 2x_1 + 2x_2 \leq 86$
- $15x_0 + 9x_3 \leq 258$
- $3x_1 + 9x_3 \leq 210$
- $15x_0 + 20x_2 \leq 237$
- $3x_1 + 20x_2 \leq 264$
- $15x_0 + 3x_1 \leq 211$
- $15x_0 + 20x_2 + 9x_3 \leq 181$
- $3x_1 + 20x_2 + 9x_3 \leq 259$

## 4: Create the Gurobi model and variables
We will now create a Gurobi model and define the variables.

## 5: Implement the objective function and constraints in Gurobi
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name="x0", lb=0)  # hours worked by Bill
x1 = m.addVar(name="x1", lb=0)  # hours worked by Dale
x2 = m.addVar(name="x2", lb=0)  # hours worked by Jean
x3 = m.addVar(name="x3", lb=0)  # hours worked by Mary

# Objective function
m.setObjective(9 * x0 + 7 * x1 + x2 + 5 * x3, gurobi.GRB.MINIMIZE)

# Constraints
# Individual constraints
m.addConstr(4 * x0 <= 139)
m.addConstr(4 * x0 <= 189)
m.addConstr(6 * x0 <= 179)
m.addConstr(15 * x0 <= 330)

m.addConstr(6 * x1 <= 139)
m.addConstr(14 * x1 <= 189)
m.addConstr(2 * x1 <= 179)
m.addConstr(3 * x1 <= 330)

m.addConstr(19 * x2 <= 139)
m.addConstr(19 * x2 <= 189)
m.addConstr(2 * x2 <= 179)
m.addConstr(20 * x2 <= 330)

m.addConstr(17 * x3 <= 139)
m.addConstr(8 * x3 <= 189)
m.addConstr(3 * x3 <= 179)
m.addConstr(9 * x3 <= 330)

# Combined constraints
m.addConstr(6 * x1 + 17 * x3 >= 26)
m.addConstr(4 * x0 + 19 * x2 >= 11)
m.addConstr(6 * x1 + 19 * x2 >= 18)
m.addConstr(4 * x0 + 6 * x1 + 19 * x2 + 17 * x3 >= 18)

m.addConstr(4 * x0 + 19 * x2 >= 36)
m.addConstr(14 * x1 + 19 * x2 >= 19)
m.addConstr(4 * x0 + 14 * x1 + 19 * x2 + 8 * x3 >= 19)

m.addConstr(6 * x0 + 3 * x3 >= 17)
m.addConstr(2 * x2 + 3 * x3 >= 42)
m.addConstr(6 * x0 + 2 * x1 >= 19)
m.addConstr(6 * x0 + 2 * x2 >= 35)
m.addConstr(2 * x1 + 2 * x2 >= 38)
m.addConstr(2 * x1 + 3 * x3 >= 38)
m.addConstr(6 * x0 + 2 * x1 + 2 * x2 + 3 * x3 >= 38)

m.addConstr(15 * x0 + 3 * x1 >= 58)
m.addConstr(15 * x0 + 9 * x3 >= 63)
m.addConstr(20 * x2 + 9 * x3 >= 74)
m.addConstr(3 * x1 + 20 * x2 >= 45)
m.addConstr(3 * x1 + 9 * x3 >= 63)
m.addConstr(15 * x0 + 20 * x2 + 9 * x3 >= 74)
m.addConstr(15 * x0 + 3 * x1 + 20 * x2 + 9 * x3 >= 74)

m.addConstr(-3 * x0 + x1 >= 0)

m.addConstr(6 * x1 + 19 * x2 <= 113)
m.addConstr(4 * x0 + 19 * x2 <= 116)
m.addConstr(6 * x1 + 17 * x3 <= 122)
m.addConstr(19 * x2 + 17 * x3 <= 85)
m.addConstr(4 * x0 + 6 * x1 <= 101)
m.addConstr(4 * x0 + 19 * x2 <= 65)
m.addConstr(4 * x0 + 19 * x2 + 17 * x3 <= 63)

m.addConstr(4 * x0 + 19 * x2 <= 104)
m.addConstr(14 * x1 + 19 * x2 <= 88)
m.addConstr(4 * x0 + 19 * x2 + 8 * x3 <= 171)
m.addConstr(4 * x0 + 14 * x1 + 19 * x2 <= 117)
m.addConstr(14 * x1 + 19 * x2 + 8 * x3 <= 72)

m.addConstr(2 * x1 + 2 * x2 <= 147)
m.addConstr(6 * x0 + 2 * x1 + 2 * x2 <= 86)

m.addConstr(15 * x0 + 9 * x3 <= 258)
m.addConstr(3 * x1 + 9 * x3 <= 210)
m.addConstr(15 * x0 + 20 * x2 <= 237)
m.addConstr(3 * x1 + 20 * x2 <= 264)
m.addConstr(15 * x0 + 3 * x1 <= 211)
m.addConstr(15 * x0 + 20 * x2 + 9 * x3 <= 181)
m.addConstr(3 * x1 + 20 * x2 + 9 * x3 <= 259)

# Solve the model
m.optimize()

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

```json
{
    'sym_variables': [
        ('x0', 'hours worked by Bill'),
        ('x1', 'hours worked by Dale'),
        ('x2', 'hours worked by Jean'),
        ('x3', 'hours worked by Mary')
    ],
    'objective_function': '9*x0 + 7*x1 + x2 + 5*x3',
    'constraints': [
        '4*x0 <= 139',
        '4*x0 <= 189',
        '6*x0 <= 179',
        '15*x0 <= 330',
        '6*x1 <= 139',
        '14*x1 <= 189',
        '2*x1 <= 179',
        '3*x1 <= 330',
        '19*x2 <= 139',
        '19*x2 <= 189',
        '2*x2 <= 179',
        '20*x2 <= 330',
        '17*x3 <= 139',
        '8*x3 <= 189',
        '3*x3 <= 179',
        '9*x3 <= 330',
        '6*x1 + 17*x3 >= 26',
        '4*x0 + 19*x2 >= 11',
        '6*x1 + 19*x2 >= 18',
        '4*x0 + 6*x1 + 19*x2 + 17*x3 >= 18',
        '4*x0 + 19*x2 >= 36',
        '14*x1 + 19*x2 >= 19',
        '4*x0 + 14*x1 + 19*x2 + 8*x3 >= 19',
        '6*x0 + 3*x3 >= 17',
        '2*x2 + 3*x3 >= 42',
        '6*x0 + 2*x1 >= 19',
        '6*x0 + 2*x2 >= 35',
        '2*x1 + 2*x2 >= 38',
        '2*x1 + 3*x3 >= 38',
        '6*x0 + 2*x1 + 2*x2 + 3*x3 >= 38',
        '15*x0 + 3*x1 >= 58',
        '15*x0 + 9*x3 >= 63',
        '20*x2 + 9*x3 >= 74',
        '3*x1 + 20*x2 >= 45',
        '3*x1 + 9*x3 >= 63',
        '15*x0 + 20*x2 + 9*x3 >= 74',
        '15*x0 + 3*x1 + 20*x2 + 9*x3 >= 74',
        '-3*x0 + x1 >= 0',
        '6*x1 + 19*x2 <= 113',
        '4*x0 + 19*x2 <= 116',
        '6*x1 + 17*x3 <= 122',
        '19*x2 + 17*x3 <= 85',
        '4*x0 + 6*x1 <= 101',
        '4*x0 + 19*x2 <= 65',
        '4*x0 + 19*x2 + 17*x3 <= 63',
        '4*x0 + 19*x2 <= 104',
        '14*x1 + 19*x2 <= 88',
        '4*x0 + 19*x2 + 8*x3 <= 171',
        '4*x0 + 14*x1 + 19*x2 <= 117',
        '14*x1 + 19*x2 + 8*x3 <= 72',
        '2*x1 + 2*x2 <= 147',
        '6*x0 + 2*x1 + 2*x2 <= 86',
        '15*x0 + 9*x3 <= 258',
        '3*x1 + 9*x3 <= 210',
        '15*x0 + 20*x2 <= 237',
        '3*x1 + 20*x2 <= 264',
        '15*x0 + 3*x1 <= 211',
        '15*x0 + 20*x2 + 9*x3 <= 181',
        '3*x1 + 20*x2 + 9*x3 <= 259'
    ]
}
```