## Step 1: Define the optimization problem and the objective function
The objective function to minimize is $7.06 \times \text{hours worked by Bobby} + 2.87 \times \text{hours worked by Paul} + 5.24 \times \text{hours worked by George}$.

## Step 2: List all the constraints
1. $\text{work quality rating of Bobby} = 18.72$
2. $\text{likelihood to quit index of Bobby} = 21.45$
3. $\text{paperwork competence rating of Bobby} = 5.23$
4. $\text{work quality rating of Paul} = 11.73$
5. $\text{likelihood to quit index of Paul} = 0.15$
6. $\text{paperwork competence rating of Paul} = 17.87$
7. $\text{work quality rating of George} = 13.63$
8. $\text{likelihood to quit index of George} = 1.88$
9. $\text{paperwork competence rating of George} = 20.72$
10. $18.72 \times \text{hours worked by Bobby} + 11.73 \times \text{hours worked by Paul} \geq 61$
11. $18.72 \times \text{hours worked by Bobby} + 11.73 \times \text{hours worked by Paul} + 13.63 \times \text{hours worked by George} \geq 61$
12. $0.15 \times \text{hours worked by Paul} + 1.88 \times \text{hours worked by George} \geq 49$
13. $21.45 \times \text{hours worked by Bobby} + 0.15 \times \text{hours worked by Paul} \geq 25$
14. $21.45 \times \text{hours worked by Bobby} + 0.15 \times \text{hours worked by Paul} + 1.88 \times \text{hours worked by George} \geq 25$
15. $5.23 \times \text{hours worked by Bobby} + 17.87 \times \text{hours worked by Paul} \geq 39$
16. $17.87 \times \text{hours worked by Paul} + 20.72 \times \text{hours worked by George} \geq 64$
17. $5.23 \times \text{hours worked by Bobby} + 20.72 \times \text{hours worked by George} \geq 56$
18. $5.23 \times \text{hours worked by Bobby} + 17.87 \times \text{hours worked by Paul} + 20.72 \times \text{hours worked by George} \geq 56$
19. $21.45 \times \text{hours worked by Bobby} + 0.15 \times \text{hours worked by Paul} \leq 87$
20. $0.15 \times \text{hours worked by Paul} + 1.88 \times \text{hours worked by George} \leq 97$
21. $\text{hours worked by Bobby}$ is not restricted to integers
22. $\text{hours worked by Paul}$ is not restricted to integers
23. $\text{hours worked by George}$ must be an integer

## 3: Formulate the problem in Gurobi
We will use Gurobi's Python API to formulate and solve this linear programming problem.

```python
import gurobi as gp

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

# Define the variables
bobby_hours = m.addVar(name="bobby_hours", lb=0)  # Not restricted to integers
paul_hours = m.addVar(name="paul_hours", lb=0)  # Not restricted to integers
george_hours = m.addVar(name="george_hours", lb=0, integrality=gp.GRB.INTEGER)  # Must be an integer

# Define the objective function
m.setObjective(7.06 * bobby_hours + 2.87 * paul_hours + 5.24 * george_hours, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(18.72 * bobby_hours + 11.73 * paul_hours >= 61)
m.addConstr(18.72 * bobby_hours + 11.73 * paul_hours + 13.63 * george_hours >= 61)
m.addConstr(0.15 * paul_hours + 1.88 * george_hours >= 49)
m.addConstr(21.45 * bobby_hours + 0.15 * paul_hours >= 25)
m.addConstr(21.45 * bobby_hours + 0.15 * paul_hours + 1.88 * george_hours >= 25)
m.addConstr(5.23 * bobby_hours + 17.87 * paul_hours >= 39)
m.addConstr(17.87 * paul_hours + 20.72 * george_hours >= 64)
m.addConstr(5.23 * bobby_hours + 20.72 * george_hours >= 56)
m.addConstr(5.23 * bobby_hours + 17.87 * paul_hours + 20.72 * george_hours >= 56)
m.addConstr(21.45 * bobby_hours + 0.15 * paul_hours <= 87)
m.addConstr(0.15 * paul_hours + 1.88 * george_hours <= 97)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Bobby hours: {bobby_hours.varValue}")
    print(f"Paul hours: {paul_hours.varValue}")
    print(f"George hours: {george_hours.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("No optimal solution found.")
```