## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Peggy' and 'hours worked by Ringo', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the symbolic representation of the resources/attributes
The resources/attributes are given as:
- $r_0$: likelihood to quit index with $x_0 = 1$, $x_1 = 5$
- $r_1$: computer competence rating with $x_0 = 6$, $x_1 = 7$

However, to accurately represent the problem, we need to associate these with the variables:
- For Peggy ($x_1$): likelihood to quit index = 1, computer competence rating = 6
- For Ringo ($x_2$): likelihood to quit index = 5, computer competence rating = 7

## 3: Formulate the objective function
The objective function to maximize is $7x_1 + 4x_2$.

## 4: Formulate the constraints
1. Peggy's likelihood to quit index: $1x_1 \geq 1$ (always true since $x_1 \geq 0$)
2. Peggy's computer competence rating: $6x_1 \geq 6$ (always true since $x_1 \geq 0$)
3. Ringo's likelihood to quit index: $5x_2 \geq 5$ (always true since $x_2 \geq 0$)
4. Ringo's computer competence rating: $7x_2 \geq 7$ (always true since $x_2 \geq 0$)
5. Total combined likelihood to quit index: $1x_1 + 5x_2 \geq 21$
6. Total combined computer competence rating: $6x_1 + 7x_2 \geq 48$
7. $3x_1 - 8x_2 \geq 0$
8. Total combined likelihood to quit index (upper bound): $1x_1 + 5x_2 \leq 44$
9. Total combined computer competence rating (upper bound): $6x_1 + 7x_2 \leq 98$

## 5: Consider variable restrictions
- $x_1$ can be fractional (continuous)
- $x_2$ must be an integer

## 6: Symbolic Representation
```json
{
'sym_variables': [('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Ringo')],
'objective_function': '7*x1 + 4*x2',
'constraints': [
    '1*x1 + 5*x2 >= 21',
    '6*x1 + 7*x2 >= 48',
    '3*x1 - 8*x2 >= 0',
    '1*x1 + 5*x2 <= 44',
    '6*x1 + 7*x2 <= 98'
]
}
```

## 7: Gurobi Code
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(lb=0, name="hours_worked_by_Peggy")  # Continuous
    x2 = model.addVar(lb=0, vtype=gurobi.GRB.INTEGER, name="hours_worked_by_Ringo")  # Integer

    # Objective function
    model.setObjective(7 * x1 + 4 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + 5 * x2 >= 21, name="likelihood_to_quit_index_min")
    model.addConstr(6 * x1 + 7 * x2 >= 48, name="computer_competence_rating_min")
    model.addConstr(3 * x1 - 8 * x2 >= 0, name="hours_worked_constraint")
    model.addConstr(x1 + 5 * x2 <= 44, name="likelihood_to_quit_index_max")
    model.addConstr(6 * x1 + 7 * x2 <= 98, name="computer_competence_rating_max")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Peggy: {x1.varValue}")
        print(f"Hours worked by Ringo: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

solve_optimization_problem()
```