## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Bobby', 'hours worked by Hank', 'hours worked by Jean', and 'hours worked by Laura'. Let's denote them 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 $8.66x_0 + 6.28x_1 + 1.06x_2 + 4.68x_3$.

## Step 3: List all the constraints in symbolic notation
1. $2x_0 \leq 85$ is not needed as it's a fixed value, instead we have:
- $x_0 \geq 0$, $x_1 \geq 0$, $x_2 \geq 0$, $x_3 \geq 0$ (non-negativity constraints, but not explicitly stated, we assume they can be negative or fractional as per problem statement)
- $13x_0 \leq 121$
- $5x_0 \leq 115$

- $13x_1 \leq 85$
- $4x_1 \leq 121$
- $10x_1 \leq 115$

- $9x_2 \leq 85$
- $5x_2 \leq 121$
- $10x_2 \leq 115$

- $1x_3 \leq 85$
- $1x_3 \leq 121$
- $12x_3 \leq 115$

Given constraints:
- $13x_1 + 9x_2 + x_3 \geq 13$
- $2x_0 + 13x_1 + 9x_2 + x_3 \geq 13$
- $13x_0 + 5x_2 \geq 28$
- $4x_1 + x_3 \geq 21$
- $5x_2 + x_3 \geq 20$
- $13x_0 + 4x_1 \geq 28$
- $4x_1 + 5x_2 + x_3 \geq 23$
- $13x_0 + 4x_1 + 5x_2 + x_3 \geq 23$
- $10x_2 + 12x_3 \geq 17$
- $5x_0 + 10x_2 \geq 15$
- $5x_0 + 10x_1 + 10x_2 + 12x_3 \geq 15$
- $4x_1 - 2x_2 \geq 0$
- $2x_0 + 9x_2 \leq 51$
- $4x_1 + 5x_2 \leq 61$
- $5x_2 + x_3 \leq 98$
- $13x_0 + 5x_2 \leq 64$
- $13x_0 + 4x_1 + x_3 \leq 77$
- $4x_1 + 5x_2 + x_3 \leq 91$
- $5x_0 + 12x_3 \leq 81$
- $10x_1 + 10x_2 \leq 74$
- $10x_1 + 12x_3 \leq 60$
- $10x_2 + 12x_3 \leq 77$
- $5x_0 + 10x_1 + 12x_3 \leq 70$
- $5x_0 + 10x_1 + 10x_2 \leq 43$

## 4: Write down the problem in a standard optimization format
Minimize $8.66x_0 + 6.28x_1 + 1.06x_2 + 4.68x_3$

Subject to:
- $13x_1 + 9x_2 + x_3 \geq 13$
- $2x_0 + 13x_1 + 9x_2 + x_3 \geq 13$
- $13x_0 + 5x_2 \geq 28$
- $4x_1 + x_3 \geq 21$
- $5x_2 + x_3 \geq 20$
- $13x_0 + 4x_1 \geq 28$
- $4x_1 + 5x_2 + x_3 \geq 23$
- $13x_0 + 4x_1 + 5x_2 + x_3 \geq 23$
- $10x_2 + 12x_3 \geq 17$
- $5x_0 + 10x_2 \geq 15$
- $5x_0 + 10x_1 + 10x_2 + 12x_3 \geq 15$
- $4x_1 - 2x_2 \geq 0$
- $2x_0 + 9x_2 \leq 51$
- $4x_1 + 5x_2 \leq 61$
- $5x_2 + x_3 \leq 98$
- $13x_0 + 5x_2 \leq 64$
- $13x_0 + 4x_1 + x_3 \leq 77$
- $4x_1 + 5x_2 + x_3 \leq 91$
- $5x_0 + 12x_3 \leq 81$
- $10x_1 + 10x_2 \leq 74$
- $10x_1 + 12x_3 \leq 60$
- $10x_2 + 12x_3 \leq 77$
- $5x_0 + 10x_1 + 12x_3 \leq 70$
- $5x_0 + 10x_1 + 10x_2 \leq 43$

## 5: Provide the symbolic representation
```json
{
    'sym_variables': [
        ['x0', 'hours worked by Bobby'],
        ['x1', 'hours worked by Hank'],
        ['x2', 'hours worked by Jean'],
        ['x3', 'hours worked by Laura']
    ],
    'objective_function': '8.66*x0 + 6.28*x1 + 1.06*x2 + 4.68*x3',
    'constraints': [
        '13*x1 + 9*x2 + x3 >= 13',
        '2*x0 + 13*x1 + 9*x2 + x3 >= 13',
        '13*x0 + 5*x2 >= 28',
        '4*x1 + x3 >= 21',
        '5*x2 + x3 >= 20',
        '13*x0 + 4*x1 >= 28',
        '4*x1 + 5*x2 + x3 >= 23',
        '13*x0 + 4*x1 + 5*x2 + x3 >= 23',
        '10*x2 + 12*x3 >= 17',
        '5*x0 + 10*x2 >= 15',
        '5*x0 + 10*x1 + 10*x2 + 12*x3 >= 15',
        '4*x1 - 2*x2 >= 0',
        '2*x0 + 9*x2 <= 51',
        '4*x1 + 5*x2 <= 61',
        '5*x2 + x3 <= 98',
        '13*x0 + 5*x2 <= 64',
        '13*x0 + 4*x1 + x3 <= 77',
        '4*x1 + 5*x2 + x3 <= 91',
        '5*x0 + 12*x3 <= 81',
        '10*x1 + 10*x2 <= 74',
        '10*x1 + 12*x3 <= 60',
        '10*x2 + 12*x3 <= 77',
        '5*x0 + 10*x1 + 12*x3 <= 70',
        '5*x0 + 10*x1 + 10*x2 <= 43'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="x0", lb=-gurobi.GRB.INFINITY)  # hours worked by Bobby
    x1 = model.addVar(name="x1", lb=-gurobi.GRB.INFINITY)  # hours worked by Hank
    x2 = model.addVar(name="x2", lb=-gurobi.GRB.INFINITY)  # hours worked by Jean
    x3 = model.addVar(name="x3", lb=-gurobi.GRB.INFINITY)  # hours worked by Laura

    # Objective function
    model.setObjective(8.66 * x0 + 6.28 * x1 + 1.06 * x2 + 4.68 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(13 * x1 + 9 * x2 + x3 >= 13)
    model.addConstr(2 * x0 + 13 * x1 + 9 * x2 + x3 >= 13)
    model.addConstr(13 * x0 + 5 * x2 >= 28)
    model.addConstr(4 * x1 + x3 >= 21)
    model.addConstr(5 * x2 + x3 >= 20)
    model.addConstr(13 * x0 + 4 * x1 >= 28)
    model.addConstr(4 * x1 + 5 * x2 + x3 >= 23)
    model.addConstr(13 * x0 + 4 * x1 + 5 * x2 + x3 >= 23)
    model.addConstr(10 * x2 + 12 * x3 >= 17)
    model.addConstr(5 * x0 + 10 * x2 >= 15)
    model.addConstr(5 * x0 + 10 * x1 + 10 * x2 + 12 * x3 >= 15)
    model.addConstr(4 * x1 - 2 * x2 >= 0)
    model.addConstr(2 * x0 + 9 * x2 <= 51)
    model.addConstr(4 * x1 + 5 * x2 <= 61)
    model.addConstr(5 * x2 + x3 <= 98)
    model.addConstr(13 * x0 + 5 * x2 <= 64)
    model.addConstr(13 * x0 + 4 * x1 + x3 <= 77)
    model.addConstr(4 * x1 + 5 * x2 + x3 <= 91)
    model.addConstr(5 * x0 + 12 * x3 <= 81)
    model.addConstr(10 * x1 + 10 * x2 <= 74)
    model.addConstr(10 * x1 + 12 * x3 <= 60)
    model.addConstr(10 * x2 + 12 * x3 <= 77)
    model.addConstr(5 * x0 + 10 * x1 + 12 * x3 <= 70)
    model.addConstr(5 * x0 + 10 * x1 + 10 * x2 <= 43)

    # Solve the model
    model.optimize()

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

optimize_problem()
```