## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Bobby', 'hours worked by Peggy', 'hours worked by George', 'hours worked by Laura'] which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the given problem into a symbolic representation
The objective function to minimize is $5.26x_0 + 4.69x_1 + 6.55x_2 + 5.86x_3$.

## Step 3: List all the constraints
1. $9x_1 + 14x_2 + 8x_3 \geq 10$ (combined paperwork from Peggy and George)
2. $2x_0 + 14x_2 + 8x_3 \geq 21$ (combined paperwork from Bobby, George, and Laura)
3. $9x_1 + 14x_2 + 8x_3 \geq 21$ (combined paperwork from Peggy, George, and Laura)
4. $2x_0 + 14x_2 + 8x_3 \geq 13$ (combined paperwork from Bobby, George, and Laura)
5. $9x_1 + 14x_2 + 8x_3 \geq 13$ (combined paperwork from Peggy, George, and Laura)
6. $2x_0 + 9x_1 + 14x_2 + 8x_3 \geq 13$ (combined paperwork from all)
7. $12x_1 + 7x_3 \geq 10$ (combined computer from Peggy and Laura)
8. $11x_0 + 3x_2 \geq 15$ (combined computer from Bobby and George)
9. $11x_0 + 12x_1 \geq 7$ (combined computer from Bobby and Peggy)
10. $12x_1 + 3x_2 + 7x_3 \geq 14$ (combined computer from Peggy, George, and Laura)
11. $11x_0 + 12x_1 + 7x_3 \geq 14$ (combined computer from Bobby, Peggy, and Laura)
12. $12x_1 + 3x_2 + 7x_3 \geq 16$ (combined computer from Peggy, George, and Laura)
13. $11x_0 + 12x_1 + 7x_3 \geq 16$ (combined computer from Bobby, Peggy, and Laura)
14. $11x_0 + 12x_1 + 3x_2 + 7x_3 \geq 16$ (combined computer from all)
15. $-2x_2 + 9x_3 \geq 0$ (relationship between George and Laura)
16. $6x_0 - 8x_1 \geq 0$ (relationship between Bobby and Peggy)
17. $9x_1 + 14x_2 \leq 77$ (paperwork from Peggy and George)
18. $14x_2 + 8x_3 \leq 34$ (paperwork from George and Laura)
19. $2x_0 + 9x_1 \leq 25$ (paperwork from Bobby and Peggy)
20. $11x_0 + 3x_2 + 7x_3 \leq 26$ (computer from Bobby, George, and Laura)

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Bobby'), 
        ('x1', 'hours worked by Peggy'), 
        ('x2', 'hours worked by George'), 
        ('x3', 'hours worked by Laura')
    ], 
    'objective_function': '5.26*x0 + 4.69*x1 + 6.55*x2 + 5.86*x3', 
    'constraints': [
        '9*x1 + 14*x2 + 8*x3 >= 10',
        '2*x0 + 14*x2 + 8*x3 >= 21',
        '9*x1 + 14*x2 + 8*x3 >= 21',
        '2*x0 + 14*x2 + 8*x3 >= 13',
        '9*x1 + 14*x2 + 8*x3 >= 13',
        '2*x0 + 9*x1 + 14*x2 + 8*x3 >= 13',
        '12*x1 + 7*x3 >= 10',
        '11*x0 + 3*x2 >= 15',
        '11*x0 + 12*x1 >= 7',
        '12*x1 + 3*x2 + 7*x3 >= 14',
        '11*x0 + 12*x1 + 7*x3 >= 14',
        '12*x1 + 3*x2 + 7*x3 >= 16',
        '11*x0 + 12*x1 + 7*x3 >= 16',
        '11*x0 + 12*x1 + 3*x2 + 7*x3 >= 16',
        '-2*x2 + 9*x3 >= 0',
        '6*x0 - 8*x1 >= 0',
        '9*x1 + 14*x2 <= 77',
        '14*x2 + 8*x3 <= 34',
        '2*x0 + 9*x1 <= 25',
        '11*x0 + 3*x2 + 7*x3 <= 26'
    ]
}
```

## 5: Implement the problem in Gurobi
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name='x0', lb=0)  # hours worked by Bobby
    x1 = model.addVar(name='x1', lb=0, integrality=1)  # hours worked by Peggy
    x2 = model.addVar(name='x2', lb=0)  # hours worked by George
    x3 = model.addVar(name='x3', lb=0)  # hours worked by Laura

    # Objective function
    model.setObjective(5.26*x0 + 4.69*x1 + 6.55*x2 + 5.86*x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(9*x1 + 14*x2 + 8*x3 >= 10)
    model.addConstr(2*x0 + 14*x2 + 8*x3 >= 21)
    model.addConstr(9*x1 + 14*x2 + 8*x3 >= 21)
    model.addConstr(2*x0 + 14*x2 + 8*x3 >= 13)
    model.addConstr(9*x1 + 14*x2 + 8*x3 >= 13)
    model.addConstr(2*x0 + 9*x1 + 14*x2 + 8*x3 >= 13)
    model.addConstr(12*x1 + 7*x3 >= 10)
    model.addConstr(11*x0 + 3*x2 >= 15)
    model.addConstr(11*x0 + 12*x1 >= 7)
    model.addConstr(12*x1 + 3*x2 + 7*x3 >= 14)
    model.addConstr(11*x0 + 12*x1 + 7*x3 >= 14)
    model.addConstr(12*x1 + 3*x2 + 7*x3 >= 16)
    model.addConstr(11*x0 + 12*x1 + 7*x3 >= 16)
    model.addConstr(11*x0 + 12*x1 + 3*x2 + 7*x3 >= 16)
    model.addConstr(-2*x2 + 9*x3 >= 0)
    model.addConstr(6*x0 - 8*x1 >= 0)
    model.addConstr(9*x1 + 14*x2 <= 77)
    model.addConstr(14*x2 + 8*x3 <= 34)
    model.addConstr(2*x0 + 9*x1 <= 25)
    model.addConstr(11*x0 + 3*x2 + 7*x3 <= 26)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print('Objective: ', model.objVal)
        print('Hours worked by Bobby: ', x0.varValue)
        print('Hours worked by Peggy: ', x1.varValue)
        print('Hours worked by George: ', x2.varValue)
        print('Hours worked by Laura: ', x3.varValue)
    else:
        print('No solution found')

solve_optimization_problem()
```