## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Hank' and 'hours worked by Jean', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the symbolic representation of the resources/attributes
The resources/attributes are given as:
- $r_0$: productivity rating
- $r_1$: work quality rating
- $r_2$: likelihood to quit index
- $r_3$: dollar cost per hour

With their respective values for Hank and Jean:
- $r_0$: $x_0 = 3.54$, $x_1 = 5.02$
- $r_1$: $x_0 = 3.9$, $x_1 = 1.19$
- $r_2$: $x_0 = 6.25$, $x_1 = 9.25$
- $r_3$: $x_0 = 3.72$, $x_1 = 4.65$

## Step 3: Formulate the objective function
The objective function to maximize is $5x_1 + 1x_2$.

## 4: Formulate the constraints
The constraints are:
1. $3.54x_1 + 5.02x_2 \geq 57$
2. $3.9x_1 + 1.19x_2 \geq 29$
3. $6.25x_1 + 9.25x_2 \geq 63$
4. $3.72x_1 + 4.65x_2 \geq 61$
5. $-6x_1 + 1x_2 \geq 0$
6. $3.54x_1 + 5.02x_2 \leq 66$
7. $3.9x_1 + 1.19x_2 \leq 93$
8. $6.25x_1 + 9.25x_2 \leq 113$
9. $3.72x_1 + 4.65x_2 \leq 116$

## 5: Symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'hours worked by Hank'), ('x2', 'hours worked by Jean')],
    'objective_function': '5*x1 + 1*x2',
    'constraints': [
        '3.54*x1 + 5.02*x2 >= 57',
        '3.9*x1 + 1.19*x2 >= 29',
        '6.25*x1 + 9.25*x2 >= 63',
        '3.72*x1 + 4.65*x2 >= 61',
        '-6*x1 + 1*x2 >= 0',
        '3.54*x1 + 5.02*x2 <= 66',
        '3.9*x1 + 1.19*x2 <= 93',
        '6.25*x1 + 9.25*x2 <= 113',
        '3.72*x1 + 4.65*x2 <= 116'
    ]
}
```

## 6: Gurobi code for the optimization problem
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="hours_worked_by_Hank", lb=0)
    x2 = model.addVar(name="hours_worked_by_Jean", lb=0)

    # Define the objective function
    model.setObjective(5 * x1 + x2, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(3.54 * x1 + 5.02 * x2 >= 57)
    model.addConstr(3.9 * x1 + 1.19 * x2 >= 29)
    model.addConstr(6.25 * x1 + 9.25 * x2 >= 63)
    model.addConstr(3.72 * x1 + 4.65 * x2 >= 61)
    model.addConstr(-6 * x1 + x2 >= 0)
    model.addConstr(3.54 * x1 + 5.02 * x2 <= 66)
    model.addConstr(3.9 * x1 + 1.19 * x2 <= 93)
    model.addConstr(6.25 * x1 + 9.25 * x2 <= 113)
    model.addConstr(3.72 * x1 + 4.65 * x2 <= 116)

    # Optimize the model
    model.optimize()

    # Print the status of the model
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Hank: {x1.varValue}")
        print(f"Hours worked by Jean: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    elif model.status == gurobi.GRB.Status.INFEASIBLE:
        print("No feasible solution exists.")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```