## Problem Description and Formulation

The problem is an optimization problem with two variables: 'hours worked by Hank' and 'hours worked by Jean'. The objective is to minimize the function 8.95 times the number of hours worked by Hank plus 2.52 multiplied by the amount of hours worked by Jean.

The problem has several constraints:
- The individual organization score, likelihood to quit index, and paperwork competence rating for Hank and Jean are fixed.
- The total combined organization score must be at least 69.
- The total combined likelihood to quit index must be at least 111.
- The total combined paperwork competence rating must be at least 51.
- A linear combination of hours worked by Hank and Jean must be non-negative.
- The total combined organization score must be less than or equal to 125.
- The total combined likelihood to quit index must be less than or equal to 274.
- The total combined paperwork competence rating must be less than or equal to 168.
- The hours worked by Hank can be a non-whole number, but the hours worked by Jean must be a non-fractional (integer) number.

## Gurobi Code Formulation

```python
import gurobipy as gp

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

# Define the variables
hours_worked_by_Hank = m.addVar(name="hours_worked_by_Hank", lb=0)  # Assuming hours cannot be negative
hours_worked_by_Jean = m.addVar(name="hours_worked_by_Jean", lb=0, integrality=gp.GRB.INTEGER)  # Jean's hours must be an integer

# Objective function: Minimize 8.95*Hank + 2.52*Jean
m.setObjective(8.95 * hours_worked_by_Hank + 2.52 * hours_worked_by_Jean, gp.GRB.MINIMIZE)

# Constraints
# Individual scores (not actually constraints since they are given and not affecting the optimization directly)
# Organization scores
org_score_Hank = 21
org_score_Jean = 13

# Likelihood to quit indices
quit_index_Hank = 30
quit_index_Jean = 4

# Paperwork competence ratings
paperwork_Hank = 27
paperwork_Jean = 28

# Total combined organization score >= 69
m.addConstraint(org_score_Hank * hours_worked_by_Hank + org_score_Jean * hours_worked_by_Jean >= 69)

# Total combined likelihood to quit index >= 111
m.addConstraint(quit_index_Hank * hours_worked_by_Hank + quit_index_Jean * hours_worked_by_Jean >= 111)

# Total combined paperwork competence rating >= 51
m.addConstraint(paperwork_Hank * hours_worked_by_Hank + paperwork_Jean * hours_worked_by_Jean >= 51)

# Linear combination: -5*Hank + 4*Jean >= 0
m.addConstraint(-5 * hours_worked_by_Hank + 4 * hours_worked_by_Jean >= 0)

# Total combined organization score <= 125
m.addConstraint(org_score_Hank * hours_worked_by_Hank + org_score_Jean * hours_worked_by_Jean <= 125)

# Total combined likelihood to quit index <= 274
m.addConstraint(quit_index_Hank * hours_worked_by_Hank + quit_index_Jean * hours_worked_by_Jean <= 274)

# Total combined paperwork competence rating <= 168
m.addConstraint(paperwork_Hank * hours_worked_by_Hank + paperwork_Jean * hours_worked_by_Jean <= 168)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Hours worked by Hank: {hours_worked_by_Hank.varValue}")
    print(f"Hours worked by Jean: {hours_worked_by_Jean.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("No optimal solution found.")
```