## Step 1: Define the optimization problem and the objective function
The goal is to minimize the objective function: $1 \times \text{hours worked by Peggy} + 5 \times \text{hours worked by Dale} + 2 \times \text{hours worked by John}$.

## Step 2: List all the constraints
1. Peggy's organization score is 20.
2. Peggy has a paperwork competence rating of 9.
3. Peggy has a productivity rating of 13.
4. Peggy's likelihood to quit index is 10.
5. Peggy has a computer competence rating of 4.
6. Dale has an organization score of 2.
7. Dale's paperwork competence rating is 6.
8. Dale has a productivity rating of 22.
9. Dale has a likelihood to quit index of 14.
10. Dale has a computer competence rating of 12.
11. John's organization score is 6.
12. John has a paperwork competence rating of 19.
13. John's productivity rating is 15.
14. John's likelihood to quit index is 12.
15. John's computer competence rating is 8.
16. The total combined organization score from hours worked by Peggy plus hours worked by John has to be 71 or more.
17. The total combined organization score from hours worked by Dale and hours worked by John has to be 34 or more.
18. The total combined organization score from hours worked by Peggy, hours worked by Dale, and hours worked by John has to be 34 or more.
19. The total combined paperwork competence rating from hours worked by Peggy and hours worked by John should be as much or more than 105.
20. The total combined paperwork competence rating from hours worked by Dale and hours worked by John should be 99 at a minimum.
21. The total combined paperwork competence rating from hours worked by Peggy plus hours worked by Dale plus hours worked by John has to be equal to or greater than 99.
22. The total combined productivity rating from hours worked by Peggy and hours worked by Dale has to be no less than 56.
23. The total combined productivity rating from hours worked by Peggy and hours worked by John should be 79 at minimum.
24. The total combined productivity rating from hours worked by Dale plus hours worked by John has to be at minimum 90.
25. The total combined productivity rating from hours worked by Peggy plus hours worked by Dale plus hours worked by John has to be 90 at a minimum.
26. The total combined likelihood to quit index from hours worked by Peggy plus hours worked by Dale has to be 105 at minimum.
27. The total combined likelihood to quit index from hours worked by Peggy plus hours worked by John must be 109 or more.
28. The total combined likelihood to quit index from hours worked by Dale and hours worked by John must be 54 or more.
29. The total combined likelihood to quit index from hours worked by Peggy, hours worked by Dale, and hours worked by John must be 88 at minimum.
30. The total combined computer competence rating from hours worked by Peggy plus hours worked by John has to be at minimum 30.
31. The total combined computer competence rating from hours worked by Peggy plus hours worked by Dale plus hours worked by John must be at minimum 30.
32. $7 \times \text{hours worked by Peggy} - 10 \times \text{hours worked by Dale} \geq 0$.
33. $-10 \times \text{hours worked by Peggy} + 5 \times \text{hours worked by John} \geq 0$.
34. The total combined paperwork competence rating from hours worked by Peggy plus hours worked by Dale should be at maximum 273.
35. The total combined paperwork competence rating from hours worked by Peggy plus hours worked by John must be 204 at maximum.
36. The total combined productivity rating from hours worked by Peggy and hours worked by Dale should be 214 or less.
37. The total combined productivity rating from hours worked by Dale and hours worked by John should be 190 at a maximum.
38. The total combined productivity rating from hours worked by Peggy, hours worked by Dale, and hours worked by John should be less than or equal to 211.
39. The total combined computer competence rating from hours worked by Dale and hours worked by John should be less than or equal to 73.
40. The total combined computer competence rating from hours worked by Peggy and hours worked by John should be at most 139.
41. The total combined computer competence rating from hours worked by Peggy plus hours worked by Dale plus hours worked by John should be 60 at maximum.

## Step 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
peggy_hours = m.addVar(name="peggy_hours", lb=0)  # hours worked by Peggy
dale_hours = m.addVar(name="dale_hours", lb=0)   # hours worked by Dale
john_hours = m.addVar(name="john_hours", lb=0)   # hours worked by John

# Objective function: Minimize 1*peggy_hours + 5*dale_hours + 2*john_hours
m.setObjective(peggy_hours + 5 * dale_hours + 2 * john_hours, gp.GRB.MINIMIZE)

# Constraints
# Fixed ratings
m.addConstraint(peggy_hours * 20 + dale_hours * 2 + john_hours * 6 >= 71)  # Organization score combined Peggy, John
m.addConstraint(dale_hours * 2 + john_hours * 6 >= 34)  # Organization score combined Dale, John
m.addConstraint(peggy_hours * 20 + dale_hours * 2 + john_hours * 6 >= 34)  # Organization score combined all

m.addConstraint(peggy_hours * 9 + john_hours * 19 >= 105)  # Paperwork competence rating combined Peggy, John
m.addConstraint(dale_hours * 6 + john_hours * 19 >= 99)  # Paperwork competence rating combined Dale, John
m.addConstraint(peggy_hours * 9 + dale_hours * 6 + john_hours * 19 >= 99)  # Paperwork competence rating combined all

m.addConstraint(peggy_hours * 13 + dale_hours * 22 >= 56)  # Productivity rating combined Peggy, Dale
m.addConstraint(peggy_hours * 13 + john_hours * 15 >= 79)  # Productivity rating combined Peggy, John
m.addConstraint(dale_hours * 22 + john_hours * 15 >= 90)  # Productivity rating combined Dale, John
m.addConstraint(peggy_hours * 13 + dale_hours * 22 + john_hours * 15 >= 90)  # Productivity rating combined all

m.addConstraint(peggy_hours * 10 + dale_hours * 14 >= 105)  # Likelihood to quit index combined Peggy, Dale
m.addConstraint(peggy_hours * 10 + john_hours * 12 >= 109)  # Likelihood to quit index combined Peggy, John
m.addConstraint(dale_hours * 14 + john_hours * 12 >= 54)  # Likelihood to quit index combined Dale, John
m.addConstraint(peggy_hours * 10 + dale_hours * 14 + john_hours * 12 >= 88)  # Likelihood to quit index combined all

m.addConstraint(peggy_hours * 4 + john_hours * 8 >= 30)  # Computer competence rating combined Peggy, John
m.addConstraint(peggy_hours * 4 + dale_hours * 12 + john_hours * 8 >= 30)  # Computer competence rating combined all

m.addConstraint(7 * peggy_hours - 10 * dale_hours >= 0)  # Constraint 32
m.addConstraint(-10 * peggy_hours + 5 * john_hours >= 0)  # Constraint 33

m.addConstraint(peggy_hours * 9 + dale_hours * 6 <= 273)  # Paperwork competence rating combined Peggy, Dale
m.addConstraint(peggy_hours * 9 + john_hours * 19 <= 204)  # Paperwork competence rating combined Peggy, John

m.addConstraint(peggy_hours * 13 + dale_hours * 22 <= 214)  # Productivity rating combined Peggy, Dale
m.addConstraint(dale_hours * 22 + john_hours * 15 <= 190)  # Productivity rating combined Dale, John
m.addConstraint(peggy_hours * 13 + dale_hours * 22 + john_hours * 15 <= 211)  # Productivity rating combined all

m.addConstraint(dale_hours * 12 + john_hours * 8 <= 73)  # Computer competence rating combined Dale, John
m.addConstraint(peggy_hours * 4 + john_hours * 8 <= 139)  # Computer competence rating combined Peggy, John
m.addConstraint(peggy_hours * 4 + dale_hours * 12 + john_hours * 8 <= 60)  # Computer competence rating combined all

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Peggy: {peggy_hours.varValue}")
    print(f"Hours worked by Dale: {dale_hours.varValue}")
    print(f"Hours worked by John: {john_hours.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```