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

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $2x_1 + 7x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $6x_1 = 6$ (Laura's work quality rating is 6, but since $r0$'s $x0$ is 6, it implies $x_1$'s coefficient is 6, however, it seems like a direct assignment rather than a constraint with $r0$'s upper bound)
- $5x_1 = 5$ (Laura's organization score is 5, similarly, $r1$'s $x0$ is 5)
- $12x_2 = 12$ (Peggy's work quality rating is 12, $r0$'s $x1$ is 12)
- $7x_2 = 7$ (Peggy's organization score is 7, $r1$'s $x1$ is 7)
- $6x_1 + 12x_2 \geq 73$ (total combined work quality rating)
- $5x_1 + 7x_2 \geq 31$ (total combined organization score)
- $-5x_1 + 8x_2 \geq 0$
- $6x_1 + 12x_2 \leq 127$ (total combined work quality rating upper bound)
- $5x_1 + 7x_2 \leq 99$ (total combined organization score upper bound)

However, upon closer inspection, the first four constraints seem to directly assign values to $x_1$ and $x_2$ rather than being constraints. Let's correct that understanding:
- The actual constraints from the problem description should directly utilize the given attributes without implying equality for $x_1$ and $x_2$ but rather use them to form the inequalities and equalities properly.

## 4: Correctly interpret constraints and form symbolic representation
Given:
- $r0 = 6x_1 + 12x_2$ for work quality rating
- $r1 = 5x_1 + 7x_2$ for organization score

Constraints:
- $6x_1 = 6$ 
- $5x_1 = 5$
- $12x_2 = 12$
- $7x_2 = 7$

These seem to directly solve for $x_1$ and $x_2$:
- $x_1 = 1$
- $x_2 = 1$

Thus, symbolic variables:
- $x_1$ for 'hours worked by Laura'
- $x_2$ for 'hours worked by Peggy'

## 5: Formulate the optimization problem in Gurobi
Given that we need to minimize $2x_1 + 7x_2$ subject to the constraints.

## 6: Write down the json representation of the problem
```json
{
'sym_variables': [('x1', 'hours worked by Laura'), ('x2', 'hours worked by Peggy')],
'objective_function': '2*x1 + 7*x2',
'constraints': [
    '6*x1 + 12*x2 >= 73',
    '5*x1 + 7*x2 >= 31',
    '-5*x1 + 8*x2 >= 0',
    '6*x1 + 12*x2 <= 127',
    '5*x1 + 7*x2 <= 99',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 7: Solve using Gurobi
```python
import gurobi

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

        # Define variables
        x1 = m.addVar(name="x1", lb=0, ub=None)  # hours worked by Laura
        x2 = m.addVar(name="x2", lb=0, ub=None)  # hours worked by Peggy

        # Objective function
        m.setObjective(2*x1 + 7*x2, gurobi.GRB.MINIMIZE)

        # Constraints
        m.addConstr(6*x1 + 12*x2 >= 73)  
        m.addConstr(5*x1 + 7*x2 >= 31)  
        m.addConstr(-5*x1 + 8*x2 >= 0)  
        m.addConstr(6*x1 + 12*x2 <= 127)  
        m.addConstr(5*x1 + 7*x2 <= 99)  

        # Solve the model
        m.optimize()

        if m.status == gurobi.GRB.Status.OPTIMAL:
            print("Optimal solution found.")
            print(f"Hours worked by Laura: {x1.varValue}")
            print(f"Hours worked by Peggy: {x2.varValue}")
            print(f"Objective: {m.objVal}")
        else:
            print("No optimal solution found.")

    except gurobi.GUROBI_ERROR as e:
        print("Gurobi Error: ", e)

solve_optimization_problem()
```