## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Laura' and 'hours worked by Bill', which we can denote as $x_0$ and $x_1$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to minimize is $9x_0 + 8x_1$.

## Step 3: List the constraints
The constraints given are:
- $11x_0 \geq 11$ (Laura's likelihood to quit index is 11, but this seems to be an equality, not an inequality, and likely a fixed value rather than a constraint)
- $13x_0 \geq 13$ (Laura's dollar cost per hour is 13, similar to above)
- $10x_0 \geq 10$ (Laura's productivity rating is 10, similar to above)
- $7x_0 \geq 7$ (Laura's computer competence rating is 7, similar to above)
- $3x_1 \geq 3$ (Bill's likelihood to quit index is 3, similar to above)
- $4x_1 \geq 4$ (Bill's dollar cost per hour is 4, similar to above)
- $14x_1 \geq 14$ (Bill's productivity rating is 14, similar to above)
- $17x_1 \geq 17$ (Bill's computer competence rating is 17, similar to above)
- $11x_0 + 3x_1 \geq 34$ (total combined likelihood to quit index)
- $13x_0 + 4x_1 \geq 13$ (total combined dollar cost per hour)
- $10x_0 + 14x_1 \geq 36$ (total combined productivity rating)
- $7x_0 + 17x_1 \geq 39$ (total combined computer competence rating)
- $-3x_0 + x_1 \geq 0$ (relationship between hours worked by Laura and Bill)
- $11x_0 + 3x_1 \leq 52$ (upper limit on total combined likelihood to quit index)
- $13x_0 + 4x_1 \leq 38$ (upper limit on total combined dollar cost per hour)
- $10x_0 + 14x_1 \leq 59$ (upper limit on total combined productivity rating)
- $7x_0 + 17x_1 \leq 77$ (upper limit on total combined computer competence rating)

## 4: Correct interpretation of given "constraints"
Upon closer inspection, the first eight "constraints" seem to be descriptive of the individuals rather than constraints on the optimization problem. Thus, we focus on the remaining inequalities.

## 5: Symbolic representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x0', 'hours worked by Laura'), ('x1', 'hours worked by Bill')],
'objective_function': '9*x0 + 8*x1',
'constraints': [
    '11*x0 + 3*x1 >= 34',
    '13*x0 + 4*x1 >= 13',
    '10*x0 + 14*x1 >= 36',
    '7*x0 + 17*x1 >= 39',
    '-3*x0 + x1 >= 0',
    '11*x0 + 3*x1 <= 52',
    '13*x0 + 4*x1 <= 38',
    '10*x0 + 14*x1 <= 59',
    '7*x0 + 17*x1 <= 77'
]
}
```

## 6: Gurobi code
Now, let's write the Gurobi code to solve this problem:
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="hours_worked_by_Laura", lb=0)  # Laura
    x1 = model.addVar(name="hours_worked_by_Bill", lb=0, integrality=gurobi.GRB.INTEGER)  # Bill

    # Objective function
    model.setObjective(9 * x0 + 8 * x1, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(11 * x0 + 3 * x1 >= 34)
    model.addConstr(13 * x0 + 4 * x1 >= 13)
    model.addConstr(10 * x0 + 14 * x1 >= 36)
    model.addConstr(7 * x0 + 17 * x1 >= 39)
    model.addConstr(-3 * x0 + x1 >= 0)
    model.addConstr(11 * x0 + 3 * x1 <= 52)
    model.addConstr(13 * x0 + 4 * x1 <= 38)
    model.addConstr(10 * x0 + 14 * x1 <= 59)
    model.addConstr(7 * x0 + 17 * x1 <= 77)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Laura: {x0.varValue}")
        print(f"Hours worked by Bill: {x1.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```