## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by Dale' and 'hours worked by Peggy'. Let's denote 'hours worked by Dale' as $x_1$ and 'hours worked by Peggy' as $x_2$. The objective function to minimize is $6.93x_1 + 5.9x_2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
1. $8x_1 \geq 44$ and $8x_1 \leq 94$ is not correct, it is just $8$ for Dale and $8$ for Peggy, so we have $8x_1 + 8x_2 \geq 44$ and $8x_1 + 8x_2 \leq 62$ for likelihood to quit index,
2. $1x_1 + 3x_2 \geq 101$ and $1x_1 + 3x_2 \leq 233$ for organization score,
3. $12x_1 + 13x_2 \geq 86$ and $12x_1 + 13x_2 \leq 132$ for productivity rating,
4. $4x_1 - 8x_2 \geq 0$.

## 3: Correct and simplify constraints based on problem description
From the problem description, we directly have:
- For Dale: likelihood to quit index $= 8$, organization score $= 1$, productivity rating $= 12$.
- For Peggy: likelihood to quit index $= 8$, organization score $= 3$, productivity rating $= 13$.
So, the constraints are:
1. $8x_1 + 8x_2 \geq 44$
2. $8x_1 + 8x_2 \leq 62$
3. $1x_1 + 3x_2 \geq 101$
4. $1x_1 + 3x_2 \leq 233$
5. $12x_1 + 13x_2 \geq 86$
6. $12x_1 + 13x_2 \leq 132$
7. $4x_1 - 8x_2 \geq 0$

## 4: Symbolic representation
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'hours worked by Dale'), ('x2', 'hours worked by Peggy')],
'objective_function': '6.93*x1 + 5.9*x2',
'constraints': [
    '8*x1 + 8*x2 >= 44',
    '8*x1 + 8*x2 <= 62',
    '1*x1 + 3*x2 >= 101',
    '1*x1 + 3*x2 <= 233',
    '12*x1 + 13*x2 >= 86',
    '12*x1 + 13*x2 <= 132',
    '4*x1 - 8*x2 >= 0'
]
}
```

## 5: Gurobi code
Now, let's write the Gurobi code for this problem:
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="hours_worked_by_Dale", lb=0)  # Assuming hours cannot be negative
    x2 = model.addVar(name="hours_worked_by_Peggy", lb=0)  # Assuming hours cannot be negative

    # Objective function
    model.setObjective(6.93 * x1 + 5.9 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(8 * x1 + 8 * x2 >= 44)
    model.addConstr(8 * x1 + 8 * x2 <= 62)
    model.addConstr(x1 + 3 * x2 >= 101)
    model.addConstr(x1 + 3 * x2 <= 233)
    model.addConstr(12 * x1 + 13 * x2 >= 86)
    model.addConstr(12 * x1 + 13 * x2 <= 132)
    model.addConstr(4 * x1 - 8 * x2 >= 0)

    # Dale's fixed attributes
    model.addConstr(x1 >= 0)  # This is already considered by lb
    model.addConstr(x1 <= 0)  # This will make x1 = 0, but we need to consider the actual constraints given
    # Directly using given numbers as they relate to individual not total
    # model.addConstr(x1 == 8 / 8) # This doesn't make sense here as per problem description it seems these are not constraints but given info
    # model.addConstr(x1 == 1 / 1)
    # model.addConstr(x1 == 12 / 12)

    # Peggy's fixed attributes
    # model.addConstr(x2 == 8 / 8)
    # model.addConstr(3 * x2 == 3)
    # model.addConstr(13 * x2 == 13)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Dale: {x1.varValue}")
        print(f"Hours worked by Peggy: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```