## Problem Description and Gurobi Code

### Problem Description

The problem is an optimization problem with three variables: 'hours worked by George', 'hours worked by Bill', and 'hours worked by Hank'. The objective function to minimize is:

9 * (hours worked by George) + 5 * (hours worked by Bill) + 9 * (hours worked by Hank)

The problem is subject to several constraints based on the likelihood to quit index and the dollar cost per hour for each individual.

### Constraints

1. The total combined likelihood to quit index from hours worked by George and Hank must be at least 19.
2. The total combined likelihood to quit index from hours worked by George and Bill must be at least 24.
3. The total combined likelihood to quit index from all three must be at least 24.
4. The total combined dollar cost per hour from hours worked by George and Hank must be at least 14.
5. The total combined dollar cost per hour from hours worked by George and Bill must be at least 6.
6. The total combined dollar cost per hour from hours worked by Bill and Hank must be at least 6.
7. The total combined dollar cost per hour from all three must be at least 6.
8. -8 * (hours worked by Bill) + 3 * (hours worked by Hank) must be at least 0.
9. The total combined likelihood to quit index from hours worked by George and Hank must be less than or equal to 39.
10. The total combined dollar cost per hour from hours worked by George and Hank must be less than or equal to 53.
11. The total combined dollar cost per hour from all three must be less than or equal to 38.

### Gurobi Code

```python
import gurobi

# Define the model
m = gurobi.Model()

# Define the variables
hours_george = m.addVar(name="hours_george", lb=0)
hours_bill = m.addVar(name="hours_bill", lb=0)
hours_hank = m.addVar(name="hours_hank", lb=0)

# Define the objective function
m.setObjective(9 * hours_george + 5 * hours_bill + 9 * hours_hank, gurobi.GRB.MINIMIZE)

# Define the constraints
m.addConstr(1 * hours_george + 4 * hours_hank >= 19)
m.addConstr(1 * hours_george + 3 * hours_bill >= 24)
m.addConstr(1 * hours_george + 3 * hours_bill + 4 * hours_hank >= 24)
m.addConstr(3 * hours_george + 1 * hours_hank >= 14)
m.addConstr(3 * hours_george + 4 * hours_bill >= 6)
m.addConstr(4 * hours_bill + 1 * hours_hank >= 6)
m.addConstr(3 * hours_george + 4 * hours_bill + 1 * hours_hank >= 6)
m.addConstr(-8 * hours_bill + 3 * hours_hank >= 0)
m.addConstr(1 * hours_george + 4 * hours_hank <= 39)
m.addConstr(3 * hours_george + 1 * hours_hank <= 53)
m.addConstr(3 * hours_george + 4 * hours_bill + 1 * hours_hank <= 38)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by George: {hours_george.varValue}")
    print(f"Hours worked by Bill: {hours_bill.varValue}")
    print(f"Hours worked by Hank: {hours_hank.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```