```json
{
  "sym_variables": [
    ("x0", "hours worked by Hank"),
    ("x1", "hours worked by Peggy"),
    ("x2", "hours worked by Paul"),
    ("x3", "hours worked by Dale")
  ],
  "objective_function": "6*x0 + 1*x1 + 1*x2 + 4*x3",
  "constraints": [
    "7*x1 + 7*x2 >= 38",
    "10*x0 + 7*x2 >= 35",
    "7*x2 + 20*x3 >= 30",
    "10*x0 + 7*x1 + 7*x2 + 20*x3 >= 30",
    "9*x0 + 15*x1 >= 25",
    "15*x1 + 23*x3 >= 29",
    "9*x0 + 21*x2 >= 37",
    "9*x0 + 21*x2 + 23*x3 >= 44",
    "9*x0 + 15*x1 + 21*x2 >= 44",
    "9*x0 + 21*x2 + 23*x3 >= 32",
    "9*x0 + 15*x1 + 21*x2 >= 32",
    "9*x0 + 15*x1 + 21*x2 + 23*x3 >= 32",
    "-9*x0 + 7*x2 >= 0",
    "7*x0 - 9*x1 >= 0",
    "10*x0 + 7*x2 + 20*x3 <= 63",
    "7*x1 + 7*x2 + 20*x3 <= 134",
    "9*x0 + 23*x3 <= 65"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    hank = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="hank")
    peggy = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="peggy")
    paul = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="paul")
    dale = model.addVar(lb=0, vtype=gp.GRB.INTEGER, name="dale")

    # Set objective function
    model.setObjective(6*hank + 1*peggy + 1*paul + 4*dale, gp.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(7*peggy + 7*paul >= 38)
    model.addConstr(10*hank + 7*paul >= 35)
    model.addConstr(7*paul + 20*dale >= 30)
    model.addConstr(10*hank + 7*peggy + 7*paul + 20*dale >= 30)
    model.addConstr(9*hank + 15*peggy >= 25)
    model.addConstr(15*peggy + 23*dale >= 29)
    model.addConstr(9*hank + 21*paul >= 37)
    model.addConstr(9*hank + 21*paul + 23*dale >= 44)
    model.addConstr(9*hank + 15*peggy + 21*paul >= 44)
    model.addConstr(9*hank + 21*paul + 23*dale >= 32)
    model.addConstr(9*hank + 15*peggy + 21*paul >= 32)
    model.addConstr(9*hank + 15*peggy + 21*paul + 23*dale >= 32)
    model.addConstr(-9*hank + 7*paul >= 0)
    model.addConstr(7*hank - 9*peggy >= 0)
    model.addConstr(10*hank + 7*paul + 20*dale <= 63)
    model.addConstr(7*peggy + 7*paul + 20*dale <= 134)
    model.addConstr(9*hank + 23*dale <= 65)


    # Optimize model
    model.optimize()

    if model.status == gp.GRB.OPTIMAL:
        print('Obj: %g' % model.objVal)
        for v in model.getVars():
            print('%s %g' % (v.varName, v.x))
    elif model.status == gp.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print(f"Optimization ended with status {model.status}")


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

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