```json
{
  "sym_variables": [
    ("x0", "hours worked by Dale"),
    ("x1", "hours worked by Jean"),
    ("x2", "hours worked by Bill")
  ],
  "objective_function": "7*x0 + 8*x1 + 3*x2",
  "constraints": [
    "9*x0 >= 0", 
    "5*x0 >= 0",
    "8*x1 >= 0",
    "6*x1 >= 0",
    "9*x2 >= 0",
    "6*x2 >= 0",
    "9*x0 + 9*x2 >= 16",
    "9*x0 + 8*x1 >= 12",
    "9*x0 + 8*x1 + 9*x2 >= 12",
    "5*x0 + 6*x2 >= 27",
    "6*x1 + 6*x2 >= 12",
    "5*x0 + 6*x1 + 6*x2 >= 12",
    "10*x0 - 3*x1 >= 0",
    "9*x0 + 8*x1 + 9*x2 <= 57",
    "5*x0 + 6*x1 + 6*x2 <= 43"
  ]
}
```

```python
import gurobipy as gp
from gurobipy import GRB

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

    # Create variables
    dale_hours = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="dale_hours")
    jean_hours = model.addVar(lb=0, vtype=GRB.INTEGER, name="jean_hours")
    bill_hours = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="bill_hours")


    # Set objective function
    model.setObjective(7 * dale_hours + 8 * jean_hours + 3 * bill_hours, GRB.MINIMIZE)

    # Add constraints
    model.addConstr(9 * dale_hours + 9 * bill_hours >= 16, "c1")
    model.addConstr(9 * dale_hours + 8 * jean_hours >= 12, "c2")
    model.addConstr(9 * dale_hours + 8 * jean_hours + 9 * bill_hours >= 12, "c3")
    model.addConstr(5 * dale_hours + 6 * bill_hours >= 27, "c4")
    model.addConstr(6 * jean_hours + 6 * bill_hours >= 12, "c5")
    model.addConstr(5 * dale_hours + 6 * jean_hours + 6 * bill_hours >= 12, "c6")
    model.addConstr(10 * dale_hours - 3 * jean_hours >= 0, "c7")
    model.addConstr(9 * dale_hours + 8 * jean_hours + 9 * bill_hours <= 57, "c8")
    model.addConstr(5 * dale_hours + 6 * jean_hours + 6 * bill_hours <= 43, "c9")


    # Optimize model
    model.optimize()

    if model.status == GRB.OPTIMAL:
        print('Obj: %g' % model.objVal)
        print('Dale Hours: %g' % dale_hours.x)
        print('Jean Hours: %g' % jean_hours.x)
        print('Bill Hours: %g' % bill_hours.x)
    elif model.status == 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')
```