```json
{
  "sym_variables": [
    ("x0", "hours worked by Peggy"),
    ("x1", "hours worked by Ringo")
  ],
  "objective_function": "7*x0 + 4*x1",
  "constraints": [
    "1*x0 = 1",
    "6*x0 = 6",
    "5*x1 = 5",
    "7*x1 = 7",
    "1*x0 + 5*x1 >= 21",
    "6*x0 + 7*x1 >= 48",
    "3*x0 - 8*x1 >= 0",
    "1*x0 + 5*x1 <= 44",
    "1*x0 + 5*x1 <= 44",
    "6*x0 + 7*x1 <= 98"
  ]
}
```

The provided problem description contains redundant constraints (e.g., the total combined likelihood to quit index being at most 44 is stated twice).  Also, the individual likelihood to quit and computer competence ratings are given as fixed values, effectively fixing the values of x0 and x1 to 1. This makes some of the other constraints potentially infeasible.  The code below checks for infeasibility and prints a message if the model is infeasible.

```python
import gurobipy as gp

try:
    # Create a new model
    model = gp.Model("optimize_work_hours")

    # Create variables
    peggy_hours = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="peggy_hours")
    ringo_hours = model.addVar(lb=0, vtype=gp.GRB.INTEGER, name="ringo_hours")

    # Set objective function
    model.setObjective(7 * peggy_hours + 4 * ringo_hours, gp.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(1 * peggy_hours == 1, "c0")
    model.addConstr(6 * peggy_hours == 6, "c1")
    model.addConstr(5 * ringo_hours == 5, "c2")
    model.addConstr(7 * ringo_hours == 7, "c3")
    model.addConstr(1 * peggy_hours + 5 * ringo_hours >= 21, "c4")
    model.addConstr(6 * peggy_hours + 7 * ringo_hours >= 48, "c5")
    model.addConstr(3 * peggy_hours - 8 * ringo_hours >= 0, "c6")
    model.addConstr(1 * peggy_hours + 5 * ringo_hours <= 44, "c7")
    model.addConstr(6 * peggy_hours + 7 * ringo_hours <= 98, "c8")


    # Optimize model
    model.optimize()

    if model.status == gp.GRB.OPTIMAL:
        print('Obj: %g' % model.objVal)
        print('Peggy Hours: %g' % peggy_hours.x)
        print('Ringo Hours: %g' % ringo_hours.x)
    elif model.status == gp.GRB.INFEASIBLE:
        print('Model is infeasible')
    else:
        print('Optimization ended with status %d' % model.status)


except gp.GurobiError as e:
    print('Error code ' + str(e.errno) + ": " + str(e))

except AttributeError:
    print('Encountered an attribute error')
```
