## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to various constraints. The variables are:
- $x_0$: hours worked by Hank
- $x_1$: hours worked by Peggy
- $x_2$: hours worked by Laura
- $x_3$: hours worked by Bill
- $x_4$: hours worked by Bobby

The objective function to maximize is: $3x_0 + 3x_1 + x_2 + 8x_3 + 7x_4$

## Step 2: List the constraints
The constraints are based on productivity ratings, work quality ratings, and dollar costs per hour for each person, as well as combined constraints.

## 3: Productivity Rating Constraints
- $4x_0 \geq 0$ (Implicit, as $x_0 \geq 0$)
- $15x_1 \geq 0$ (Implicit, as $x_1 \geq 0$)
- $12x_2 \geq 0$ (Implicit, as $x_2 \geq 0$)
- $17x_3 \geq 0$ (Implicit, as $x_3 \geq 0$)
- $5x_4 \geq 0$ (Implicit, as $x_4 \geq 0$)
- $12x_2 + 5x_4 \geq 59$
- $12x_2 + 17x_3 \geq 53$
- $15x_1 + 17x_3 \geq 133$
- $17x_3 + 5x_4 \geq 54$
- $4x_0 + 5x_4 \geq 74$
- $4x_0 + 15x_1 + 12x_2 \geq 113$
- $4x_0 + 12x_2 + 17x_3 \geq 113$
- $4x_0 + 15x_1 + 17x_3 \geq 113$
- $12x_2 + 17x_3 + 5x_4 \geq 113$
- $15x_1 + 12x_2 + 17x_3 \geq 113$
- $4x_0 + 15x_1 + 12x_2 \geq 98$
- $4x_0 + 12x_2 + 17x_3 \geq 98$
- $4x_0 + 15x_1 + 17x_3 \geq 98$
- $12x_2 + 17x_3 + 5x_4 \geq 98$
- $15x_1 + 12x_2 + 17x_3 \geq 98$
- $4x_0 + 15x_1 + 12x_2 \geq 124$
- $4x_0 + 12x_2 + 17x_3 \geq 124$
- $4x_0 + 15x_1 + 17x_3 \geq 124$
- $12x_2 + 17x_3 + 5x_4 \geq 124$
- $15x_1 + 12x_2 + 17x_3 \geq 124$
- $4x_0 + 15x_1 + 12x_2 \geq 149$
- $4x_0 + 12x_2 + 17x_3 \geq 149$
- $4x_0 + 15x_1 + 17x_3 \geq 149$
- $12x_2 + 17x_3 + 5x_4 \geq 149$
- $15x_1 + 12x_2 + 17x_3 \geq 149$

## 4: Work Quality Rating Constraints
- $23x_0 + 21x_1 + x_2 + 9x_3 + 16x_4 \geq 54$
- $21x_1 + x_2 + 16x_4 \geq 54$
- $21x_1 + x_2 + 9x_3 \geq 54$
- $x_2 + 9x_3 + 16x_4 \geq 54$
- $23x_0 + 21x_1 + 9x_3 \geq 58$
- $21x_1 + x_2 + 16x_4 \geq 58$
- $21x_1 + x_2 + 9x_3 \geq 58$
- $x_2 + 9x_3 + 16x_4 \geq 58$
- $23x_0 + 21x_1 + 9x_3 \geq 61$
- $21x_1 + x_2 + 16x_4 \geq 61$
- $21x_1 + x_2 + 9x_3 \geq 61$
- $x_2 + 9x_3 + 16x_4 \geq 61$

## 5: Dollar Cost per Hour Constraints
- $19x_1 + 22x_3 \geq 69$
- $22x_3 + 19x_4 \geq 122$
- $19x_1 + 19x_4 \geq 102$
- $15x_0 + 22x_3 \geq 117$
- $15x_0 + 19x_1 \geq 119$
- $19x_1 + 18x_2 \geq 107$
- $15x_0 + 18x_2 \geq 75$
- $19x_1 + 22x_3 + 19x_4 \geq 109$
- $15x_0 + 19x_1 + 18x_2 \geq 109$
- $19x_1 + 18x_2 + 22x_3 \geq 109$
- $15x_0 + 18x_2 + 22x_3 \geq 109$
- $15x_0 + 19x_1 + 22x_3 \geq 109$

## 6: Upper Bound Constraints
- $15x_0 \leq 748$
- $19x_1 \leq 415$
- $18x_2 \leq 639$
- $22x_3 \leq 639$
- $19x_4 \leq 639$

## 7: Symbolic Representation
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Hank'),
        ('x1', 'hours worked by Peggy'),
        ('x2', 'hours worked by Laura'),
        ('x3', 'hours worked by Bill'),
        ('x4', 'hours worked by Bobby')
    ],
    'objective_function': '3*x0 + 3*x1 + x2 + 8*x3 + 7*x4',
    'constraints': [
        '4*x0 + 15*x1 + 12*x2 >= 113',
        '4*x0 + 12*x2 + 17*x3 >= 113',
        '4*x0 + 15*x1 + 17*x3 >= 113',
        '12*x2 + 17*x3 + 5*x4 >= 113',
        '15*x1 + 12*x2 + 17*x3 >= 113',
        '4*x0 + 15*x1 + 12*x2 >= 98',
        '4*x0 + 12*x2 + 17*x3 >= 98',
        '4*x0 + 15*x1 + 17*x3 >= 98',
        '12*x2 + 17*x3 + 5*x4 >= 98',
        '15*x1 + 12*x2 + 17*x3 >= 98',
        '4*x0 + 15*x1 + 12*x2 >= 124',
        '4*x0 + 12*x2 + 17*x3 >= 124',
        '4*x0 + 15*x1 + 17*x3 >= 124',
        '12*x2 + 17*x3 + 5*x4 >= 124',
        '15*x1 + 12*x2 + 17*x3 >= 124',
        '4*x0 + 15*x1 + 12*x2 >= 149',
        '4*x0 + 12*x2 + 17*x3 >= 149',
        '4*x0 + 15*x1 + 17*x3 >= 149',
        '12*x2 + 17*x3 + 5*x4 >= 149',
        '15*x1 + 12*x2 + 17*x3 >= 149',
        '23*x0 + 21*x1 + x2 + 9*x3 + 16*x4 >= 54',
        '19*x1 + 22*x3 >= 69',
        '22*x3 + 19*x4 >= 122',
        '15*x0 <= 748',
        '19*x1 <= 415',
        '18*x2 <= 639',
        '22*x3 <= 639',
        '19*x4 <= 639'
    ]
}
```

## Step 8: Gurobi Code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(lb=0, name="x0")  # hours worked by Hank
    x1 = model.addVar(lb=0, name="x1")  # hours worked by Peggy
    x2 = model.addVar(lb=0, name="x2")  # hours worked by Laura
    x3 = model.addVar(lb=0, name="x3")  # hours worked by Bill
    x4 = model.addVar(lb=0, name="x4")  # hours worked by Bobby

    # Objective function
    model.setObjective(3*x0 + 3*x1 + x2 + 8*x3 + 7*x4, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(4*x0 + 15*x1 + 12*x2 >= 113)
    model.addConstr(4*x0 + 12*x2 + 17*x3 >= 113)
    model.addConstr(4*x0 + 15*x1 + 17*x3 >= 113)
    model.addConstr(12*x2 + 17*x3 + 5*x4 >= 113)
    model.addConstr(15*x1 + 12*x2 + 17*x3 >= 113)
    model.addConstr(4*x0 + 15*x1 + 12*x2 >= 98)
    model.addConstr(4*x0 + 12*x2 + 17*x3 >= 98)
    model.addConstr(4*x0 + 15*x1 + 17*x3 >= 98)
    model.addConstr(12*x2 + 17*x3 + 5*x4 >= 98)
    model.addConstr(15*x1 + 12*x2 + 17*x3 >= 98)
    model.addConstr(4*x0 + 15*x1 + 12*x2 >= 124)
    model.addConstr(4*x0 + 12*x2 + 17*x3 >= 124)
    model.addConstr(4*x0 + 15*x1 + 17*x3 >= 124)
    model.addConstr(12*x2 + 17*x3 + 5*x4 >= 124)
    model.addConstr(15*x1 + 12*x2 + 17*x3 >= 124)
    model.addConstr(4*x0 + 15*x1 + 12*x2 >= 149)
    model.addConstr(4*x0 + 12*x2 + 17*x3 >= 149)
    model.addConstr(4*x0 + 15*x1 + 17*x3 >= 149)
    model.addConstr(12*x2 + 17*x3 + 5*x4 >= 149)
    model.addConstr(15*x1 + 12*x2 + 17*x3 >= 149)
    model.addConstr(23*x0 + 21*x1 + x2 + 9*x3 + 16*x4 >= 54)
    model.addConstr(19*x1 + 22*x3 >= 69)
    model.addConstr(22*x3 + 19*x4 >= 122)
    model.addConstr(15*x0 <= 748)
    model.addConstr(19*x1 <= 415)
    model.addConstr(18*x2 <= 639)
    model.addConstr(22*x3 <= 639)
    model.addConstr(19*x4 <= 639)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Hank: ", x0.varValue)
        print("Hours worked by Peggy: ", x1.varValue)
        print("Hours worked by Laura: ", x2.varValue)
        print("Hours worked by Bill: ", x3.varValue)
        print("Hours worked by Bobby: ", x4.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```