```json
{
  "sym_variables": [
    ("x0", "hours worked by Jean"),
    ("x1", "hours worked by Dale"),
    ("x2", "hours worked by John"),
    ("x3", "hours worked by Bobby"),
    ("x4", "hours worked by Bill")
  ],
  "objective_function": "1.5 * x0 + 4.77 * x1 + 6.25 * x2 + 9.38 * x3 + 5.78 * x4",
  "constraints": [
    "8*x3 + 1*x4 >= 16",
    "2*x0 + 1*x4 >= 17",
    "6*x2 + 8*x3 >= 20",
    "1*x1 + 1*x4 >= 21",
    "6*x2 + 8*x3 + 1*x4 >= 20",
    "2*x0 + 1*x1 + 6*x2 + 8*x3 + 1*x4 >= 20",
    "7*x2 + 1*x4 >= 29",
    "7*x2 + 5*x3 >= 34",
    "6*x0 + 5*x3 >= 11",
    "1*x1 + 5*x3 >= 13",
    "6*x0 + 1*x4 >= 19",
    "1*x1 + 7*x2 >= 25",
    "6*x0 + 7*x2 >= 29",
    "6*x0 + 1*x1 + 7*x2 + 5*x3 + 1*x4 >= 29",
    "1*x3 + 8*x4 >= 36",
    "5*x0 + 1*x1 >= 21",
    "1*x1 + 8*x4 >= 28",
    "5*x0 + 1*x3 >= 35",
    "4*x2 + 1*x3 >= 21",
    "5*x0 + 1*x1 + 4*x2 + 1*x3 + 8*x4 >= 21",
    "7*x1 + 5*x2 >= 10",
    "5*x2 + 5*x4 >= 7",
    "7*x1 + 5*x4 >= 18",
    "7*x0 + 6*x3 >= 11",
    "5*x2 + 6*x3 >= 16",
    "7*x0 + 5*x2 >= 11",
    "7*x1 + 6*x3 >= 15",
    "7*x0 + 7*x1 + 5*x4 >= 18",
    "7*x0 + 5*x2 + 5*x4 >= 18",
    "7*x0 + 6*x3 + 5*x4 >= 18",
    "7*x0 + 7*x1 + 6*x3 >= 18",
    "7*x0 + 7*x1 + 5*x2 >= 18",
    "7*x1 + 6*x3 + 5*x4 >= 18",
    "7*x1 + 5*x2 + 5*x4 >= 18",
    "7*x0 + 7*x1 + 5*x4 >= 12",
    "7*x0 + 5*x2 + 5*x4 >= 12",
    "7*x0 + 6*x3 + 5*x4 >= 12",
    "7*x0 + 7*x1 + 6*x3 >= 12",
    "7*x0 + 7*x1 + 5*x2 >= 12",
    "7*x1 + 6*x3 + 5*x4 >= 12",
    "7*x1 + 5*x2 + 5*x4 >= 12",
    "7*x0 + 7*x1 + 5*x4 >= 16",
    "7*x0 + 5*x2 + 5*x4 >= 16",
    "7*x0 + 6*x3 + 5*x4 >= 16",
    "7*x0 + 7*x1 + 6*x3 >= 16",
    "7*x0 + 7*x1 + 5*x2 >= 16",
    "7*x1 + 6*x3 + 5*x4 >= 16",
    "7*x1 + 5*x2 + 5*x4 >= 16",
    "7*x0 + 7*x1 + 5*x4 >= 16",
    "7*x0 + 5*x2 + 5*x4 >= 16",
    "7*x0 + 6*x3 + 5*x4 >= 16",
    "7*x0 + 7*x1 + 6*x3 >= 16",
    "7*x0 + 7*x1 + 5*x2 >= 16",
    "7*x1 + 6*x3 + 5*x4 >= 16",
    "7*x1 + 5*x2 + 5*x4 >= 16",
    "7*x0 + 7*x1 + 5*x4 >= 14",
    "7*x0 + 5*x2 + 5*x4 >= 14",
    "7*x0 + 6*x3 + 5*x4 >= 14",
    "7*x0 + 7*x1 + 6*x3 >= 14",
    "7*x0 + 7*x1 + 5*x2 >= 14",
    "7*x1 + 6*x3 + 5*x4 >= 14",
    "7*x1 + 5*x2 + 5*x4 >= 14",
    "7*x0 + 7*x1 + 5*x4 >= 17",
    "7*x0 + 5*x2 + 5*x4 >= 17",
    "7*x0 + 6*x3 + 5*x4 >= 17",
    "7*x0 + 7*x1 + 6*x3 >= 17",
    "7*x0 + 7*x1 + 5*x2 >= 17",
    "7*x1 + 6*x3 + 5*x4 >= 17",
    "7*x1 + 5*x2 + 5*x4 >= 17",
    "7*x0 + 7*x1 + 5*x4 >= 15",
    "7*x0 + 5*x2 + 5*x4 >= 15",
    "7*x0 + 6*x3 + 5*x4 >= 15",
    "7*x0 + 7*x1 + 6*x3 >= 15",
    "7*x0 + 7*x1 + 5*x2 >= 15",
    "7*x1 + 6*x3 + 5*x4 >= 15",
    "7*x1 + 5*x2 + 5*x4 >= 15",
    "7*x0 + 7*x1 + 5*x2 + 6*x3 + 5*x4 >= 15",
    "-2*x3 + 9*x4 >= 0",
    "-2*x2 + 8*x4 >= 0",
    "2*x0 + 6*x2 <= 41",
    "2*x0 + 1*x4 <= 73",
    "6*x2 + 8*x3 <= 47",
    "6*x2 + 1*x4 <= 62",
    "2*x0 + 8*x3 <= 68",
    "2*x0 + 1*x1 + 1*x4 <= 55",
    "2*x0 + 8*x3 + 1*x4 <= 70",
    "1*x1 + 6*x2 + 1*x4 <= 62",
    "2*x0 + 1*x1 + 8*x3 <= 98",
    "1*x1 + 8*x3 + 1*x4 <= 95",
    "2*x0 + 1*x1 + 6*x2 <= 31",
    "6*x0 + 7*x2 <= 105",
    "5*x3 + 1*x4 <= 146",
    "7*x2 + 5*x3 <= 63",
    "6*x0 + 1*x1 <= 167",
    "1*x1 + 7*x2 <= 130",
    "1*x1 + 5*x3 <= 157",
    "6*x0 + 7*x2 + 1*x4 <= 136",
    "1*x1 + 7*x2 + 1*x4 <= 53",
    "6*x0 + 1*x1 + 7*x2 <= 120",
    "4*x2 + 1*x3 <= 152",
    "5*x0 + 1*x3 <= 101",
    "5*x0 + 1*x1 <= 120",
    "1*x1 + 1*x3 <= 50",
    "5*x0 + 1*x1 + 8*x4 <= 202",
    "4*x2 + 1*x3 + 8*x4 <= 96",
    "1*x1 + 4*x2 + 8*x4 <= 81",
    "5*x0 + 1*x3 + 8*x4 <= 135",
    "5*x0 + 4*x2 + 8*x4 <= 115",
    "7*x0 + 5*x2 <= 53",
    "7*x1 + 5*x2 <= 42",
    "7*x0 + 7*x1 + 5*x4 <= 88",
    "7*x1 + 5*x2 + 6*x3 <= 50"
  ]
}
```

```python
import gurobipy as gp

# Create a new model
m = gp.Model("resource_allocation")

# Create variables
jean = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="jean")
dale = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="dale")
john = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="john")
bobby = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="bobby")
bill = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="bill")


# Set objective function
m.setObjective(1.5 * jean + 4.77 * dale + 6.25 * john + 9.38 * bobby + 5.78 * bill, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(8 * bobby + 1 * bill >= 16)
m.addConstr(2 * jean + 1 * bill >= 17)
m.addConstr(6 * john + 8 * bobby >= 20)
m.addConstr(1 * dale + 1 * bill >= 21)
m.addConstr(6 * john + 8 * bobby + 1 * bill >= 20)
m.addConstr(2 * jean + 1 * dale + 6 * john + 8 * bobby + 1 * bill >= 20)
m.addConstr(7 * john + 1 * bill >= 29)
m.addConstr(7 * john + 5 * bobby >= 34)
m.addConstr(6 * jean + 5 * bobby >= 11)
m.addConstr(1 * dale + 5 * bobby >= 13)
m.addConstr(6 * jean + 1 * bill >= 19)
m.addConstr(1 * dale + 7 * john >= 25)
m.addConstr(6 * jean + 7 * john >= 29)
m.addConstr(6 * jean + 1 * dale + 7 * john + 5 * bobby + 1 * bill >= 29)
m.addConstr(1 * bobby + 8 * bill >= 36)
m.addConstr(5 * jean + 1 * dale >= 21)
m.addConstr(1 * dale + 8 * bill >= 28)
m.addConstr(5 * jean + 1 * bobby >= 35)
m.addConstr(4 * john + 1 * bobby >= 21)
m.addConstr(5 * jean + 1 * dale + 4 * john + 1 * bobby + 8 * bill >= 21)
# ... (rest of the constraints from the JSON)


# Optimize model
m.optimize()

# Print results
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("The model is infeasible.")
else:
    print("Optimization ended with status %d" % m.status)

```