```json
{
  "sym_variables": [
    ("x0", "hours worked by Hank"),
    ("x1", "hours worked by Laura"),
    ("x2", "hours worked by George"),
    ("x3", "hours worked by Jean"),
    ("x4", "hours worked by Dale")
  ],
  "objective_function": "3.24*x0 + 2.29*x1 + 1.49*x2 + 1.05*x3 + 9.73*x4",
  "constraints": [
    "3.51*x0 + 1.84*x3 >= 41",
    "11.46*x1 + 1.84*x3 >= 60",
    "3.51*x0 + 11.46*x1 >= 43",
    "1.84*x3 + 7.1*x4 >= 64",
    "9.55*x2 + 1.84*x3 >= 64",
    "3.51*x0 + 9.55*x2 >= 58",
    "3.51*x0 + 7.1*x4 >= 32",
    "3.51*x0 + 9.55*x2 + 7.1*x4 >= 51",
    "3.51*x0 + 11.46*x1 + 9.55*x2 >= 51",
    "3.51*x0 + 1.84*x3 + 7.1*x4 >= 51",
    "9.55*x2 + 1.84*x3 + 7.1*x4 >= 51",
    "3.51*x0 + 9.55*x2 + 7.1*x4 >= 53",
    "3.51*x0 + 11.46*x1 + 9.55*x2 >= 53",
    "3.51*x0 + 1.84*x3 + 7.1*x4 >= 53",
    "9.55*x2 + 1.84*x3 + 7.1*x4 >= 53",
    "3.51*x0 + 9.55*x2 + 7.1*x4 >= 62",
    "3.51*x0 + 11.46*x1 + 9.55*x2 >= 62",
    "3.51*x0 + 1.84*x3 + 7.1*x4 >= 62",
    "9.55*x2 + 1.84*x3 + 7.1*x4 >= 62",
    "3.51*x0 + 9.55*x2 + 7.1*x4 >= 50",
    "3.51*x0 + 11.46*x1 + 9.55*x2 >= 50",
    "3.51*x0 + 1.84*x3 + 7.1*x4 >= 50",
    "9.55*x2 + 1.84*x3 + 7.1*x4 >= 50",
    "3.51*x0 + 11.46*x1 + 9.55*x2 + 1.84*x3 + 7.1*x4 >= 50",
    "2.86*x0 + 5.09*x4 >= 61",
    "12.88*x1 + 5.09*x4 >= 48",
    "12.88*x1 + 7.15*x3 >= 43",
    "2.86*x0 + 12.88*x1 + 4.78*x2 + 7.15*x3 + 5.09*x4 >= 43",
    "-5*x0 + 3*x2 >= 0",
    "-5*x3 + 3*x4 >= 0",
    "3.51*x0 + 11.46*x1 + 9.55*x2 <= 208",
    "2.86*x0 + 4.78*x2 <= 264",
    "2.86*x0 + 12.88*x1 <= 94",
    "2.86*x0 + 5.09*x4 <= 298",
    "7.15*x3 + 5.09*x4 <= 245",
    "2.86*x0 + 7.15*x3 <= 253",
    "4.78*x2 + 7.15*x3 <= 379",
    "12.88*x1 + 5.09*x4 <= 163",
    "12.88*x1 + 7.15*x3 <= 205",
    "2.86*x0 + 7.15*x3 + 5.09*x4 <= 192",
    "2.86*x0 + 12.88*x1 + 4.78*x2 <= 388",
    "2.86*x0 + 12.88*x1 + 7.15*x3 <= 158",
    "2.86*x0 + 4.78*x2 + 7.15*x3 <= 82",
    "4.78*x2 + 7.15*x3 + 5.09*x4 <= 139",
    "2.86*x0 + 4.78*x2 + 5.09*x4 <= 90",
    "x1 == int"  
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    hank = m.addVar(name="hank")
    laura = m.addVar(name="laura", vtype=gp.GRB.INTEGER)
    george = m.addVar(name="george")
    jean = m.addVar(name="jean")
    dale = m.addVar(name="dale")

    # Set objective function
    m.setObjective(3.24 * hank + 2.29 * laura + 1.49 * george + 1.05 * jean + 9.73 * dale, gp.GRB.MINIMIZE)

    # Add constraints
    m.addConstr(3.51 * hank + 1.84 * jean >= 41)
    m.addConstr(11.46 * laura + 1.84 * jean >= 60)
    m.addConstr(3.51 * hank + 11.46 * laura >= 43)
    m.addConstr(1.84 * jean + 7.1 * dale >= 64)
    m.addConstr(9.55 * george + 1.84 * jean >= 64)
    m.addConstr(3.51 * hank + 9.55 * george >= 58)
    m.addConstr(3.51 * hank + 7.1 * dale >= 32)
    m.addConstr(3.51 * hank + 9.55 * george + 7.1 * dale >= 51)
    m.addConstr(3.51 * hank + 11.46 * laura + 9.55 * george >= 51)
    m.addConstr(3.51 * hank + 1.84 * jean + 7.1 * dale >= 51)
    m.addConstr(9.55 * george + 1.84 * jean + 7.1 * dale >= 51)
    m.addConstr(3.51 * hank + 9.55 * george + 7.1 * dale >= 53)
    m.addConstr(3.51 * hank + 11.46 * laura + 9.55 * george >= 53)
    m.addConstr(3.51 * hank + 1.84 * jean + 7.1 * dale >= 53)
    m.addConstr(9.55 * george + 1.84 * jean + 7.1 * dale >= 53)
    m.addConstr(3.51 * hank + 9.55 * george + 7.1 * dale >= 62)
    m.addConstr(3.51 * hank + 11.46 * laura + 9.55 * george >= 62)
    m.addConstr(3.51 * hank + 1.84 * jean + 7.1 * dale >= 62)
    m.addConstr(9.55 * george + 1.84 * jean + 7.1 * dale >= 62)
    m.addConstr(3.51 * hank + 9.55 * george + 7.1 * dale >= 50)
    m.addConstr(3.51 * hank + 11.46 * laura + 9.55 * george >= 50)
    m.addConstr(3.51 * hank + 1.84 * jean + 7.1 * dale >= 50)
    m.addConstr(9.55 * george + 1.84 * jean + 7.1 * dale >= 50)
    m.addConstr(3.51 * hank + 11.46 * laura + 9.55 * george + 1.84 * jean + 7.1 * dale >= 50)
    m.addConstr(2.86 * hank + 5.09 * dale >= 61)
    m.addConstr(12.88 * laura + 5.09 * dale >= 48)
    m.addConstr(12.88 * laura + 7.15 * jean >= 43)
    m.addConstr(2.86 * hank + 12.88 * laura + 4.78 * george + 7.15 * jean + 5.09 * dale >= 43)
    m.addConstr(-5 * hank + 3 * george >= 0)
    m.addConstr(-5 * jean + 3 * dale >= 0)
    m.addConstr(3.51 * hank + 11.46 * laura + 9.55 * george <= 208)
    m.addConstr(2.86 * hank + 4.78 * george <= 264)
    m.addConstr(2.86 * hank + 12.88 * laura <= 94)
    m.addConstr(2.86 * hank + 5.09 * dale <= 298)
    m.addConstr(7.15 * jean + 5.09 * dale <= 245)
    m.addConstr(2.86 * hank + 7.15 * jean <= 253)
    m.addConstr(4.78 * george + 7.15 * jean <= 379)
    m.addConstr(12.88 * laura + 5.09 * dale <= 163)
    m.addConstr(12.88 * laura + 7.15 * jean <= 205)
    m.addConstr(2.86 * hank + 7.15 * jean + 5.09 * dale <= 192)
    m.addConstr(2.86 * hank + 12.88 * laura + 4.78 * george <= 388)
    m.addConstr(2.86 * hank + 12.88 * laura + 7.15 * jean <= 158)
    m.addConstr(2.86 * hank + 4.78 * george + 7.15 * jean <= 82)
    m.addConstr(4.78 * george + 7.15 * jean + 5.09 * dale <= 139)
    m.addConstr(2.86 * hank + 4.78 * george + 5.09 * dale <= 90)


    # Optimize model
    m.optimize()

    if m.status == gp.GRB.OPTIMAL:
        print('Obj: %g' % m.objVal)
        for v in m.getVars():
            print('%s %g' % (v.varName, v.x))
    elif m.status == gp.GRB.INFEASIBLE:
        print('Optimization was infeasible.')


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

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