## Problem Description and Gurobi Code

The problem is an optimization problem with a linear objective function and linear constraints. The goal is to maximize the objective function subject to the given constraints.

### Objective Function

The objective function to be maximized is:
\[ 6.63 \times \text{hours worked by Paul} + 4.33 \times \text{hours worked by Bill} + 2.22 \times \text{hours worked by George} + 7.29 \times \text{hours worked by Hank} + 2.29 \times \text{hours worked by John} + 6.9 \times \text{hours worked by Ringo} + 1.01 \times \text{hours worked by Jean} \]

### Constraints

The constraints are:
- The computer competence rating for each individual is given and fixed.
- The total combined computer competence rating from hours worked by George plus hours worked by Jean has to be equal to or greater than 13.
- The total combined computer competence rating from hours worked by Paul, and hours worked by John has to be greater than or equal to 22.
- The total combined computer competence rating from hours worked by George, and hours worked by Ringo has to be greater than or equal to 12.
- The total combined computer competence rating from hours worked by Bill, and hours worked by Hank has to be 28 at minimum.
- The total combined computer competence rating from hours worked by Bill plus hours worked by George has to be at minimum 13.
- The total combined computer competence rating from hours worked by Hank plus hours worked by Ringo must be greater than or equal to 20.
- The total combined computer competence rating from hours worked by Ringo, and hours worked by Jean must be 17 at a minimum.
- The total combined computer competence rating from hours worked by Paul plus hours worked by Hank should be as much or more than 26.
- The total combined computer competence rating from hours worked by John, and hours worked by Ringo has to be 27 at minimum.
- The total combined computer competence rating from hours worked by Paul, and hours worked by Jean should be greater than or equal to 11.
- The total combined computer competence rating from hours worked by George plus hours worked by Hank should be 183 at maximum.
- The total combined computer competence rating from hours worked by George and hours worked by Ringo should be no more than 198.
- The total combined computer competence rating from hours worked by John plus hours worked by Jean has to be no more than 96.
- The total combined computer competence rating from hours worked by Ringo plus hours worked by Jean must be 33 or less.
- The total combined computer competence rating from hours worked by John plus hours worked by Ringo should be as much or less than 167.
- The total combined computer competence rating from hours worked by Paul plus hours worked by Ringo must be equal to or less than 71.
- The total combined computer competence rating from hours worked by Hank and hours worked by John has to be equal to or less than 64.
- The total combined computer competence rating from hours worked by Hank, and hours worked by Ringo must be less than or equal to 52.
- The total combined computer competence rating from hours worked by Paul plus hours worked by Hank has to be 138 at a maximum.
- The total combined computer competence rating from hours worked by Paul, and hours worked by George has to be equal to or less than 49.
- The total combined computer competence rating from hours worked by Bill and hours worked by George has to be equal to or less than 36.
- The total combined computer competence rating from hours worked by Bill plus hours worked by George plus hours worked by Hank must be 75 at maximum.
- The total combined computer competence rating from hours worked by George, hours worked by Hank, and hours worked by Ringo should be less than or equal to 165.
- The total combined computer competence rating from hours worked by Hank, hours worked by Ringo, and hours worked by Jean must be 205 at a maximum.
- The total combined computer competence rating from hours worked by Bill plus hours worked by George plus hours worked by John must be equal to or less than 93.
- The total combined computer competence rating from hours worked by Paul, hours worked by Hank, and hours worked by Ringo has to be 192 or less.
- The total combined computer competence rating from hours worked by Paul, hours worked by Bill and hours worked by Jean should be 101 at a maximum.
- The total combined computer competence rating from hours worked by George, hours worked by John, and hours worked by Jean should be 140 at a maximum.
- The total combined computer competence rating from hours worked by Paul plus hours worked by Ringo plus hours worked by Jean has to be equal to or less than 208.
- The total combined computer competence rating from hours worked by Hank, hours worked by John, and hours worked by Jean must be less than or equal to 76.
- The total combined computer competence rating from hours worked by Bill, hours worked by John and hours worked by Jean must be 151 at maximum.
- The total combined computer competence rating from hours worked by Paul plus hours worked by Bill plus hours worked by George plus hours worked by Hank plus hours worked by John plus hours worked by Ringo plus hours worked by Jean should be 151 or less.

### Gurobi Code

```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
hours_worked_by_Paul = model.addVar(name="hours_worked_by_Paul", lb=0)
hours_worked_by_Bill = model.addVar(name="hours_worked_by_Bill", lb=0)
hours_worked_by_George = model.addVar(name="hours_worked_by_George", lb=0)
hours_worked_by_Hank = model.addVar(name="hours_worked_by_Hank", lb=0)
hours_worked_by_John = model.addVar(name="hours_worked_by_John", lb=0)
hours_worked_by_Ringo = model.addVar(name="hours_worked_by_Ringo", lb=0)
hours_worked_by_Jean = model.addVar(name="hours_worked_by_Jean", lb=0)

# Objective function coefficients
obj_coeffs = [6.63, 4.33, 2.22, 7.29, 2.29, 6.9, 1.01]
model.setObjective(obj_coeffs[0]*hours_worked_by_Paul + obj_coeffs[1]*hours_worked_by_Bill + 
                   obj_coeffs[2]*hours_worked_by_George + obj_coeffs[3]*hours_worked_by_Hank + 
                   obj_coeffs[4]*hours_worked_by_John + obj_coeffs[5]*hours_worked_by_Ringo + 
                   obj_coeffs[6]*hours_worked_by_Jean, gurobi.GRB.MAXIMIZE)

# Constraints
# Computer competence ratings
computer_competence_ratings = {'Paul': 8, 'Bill': 11, 'George': 2, 'Hank': 2, 
                              'John': 11, 'Ringo': 6, 'Jean': 11}

# Constraints
model.addConstr(2*hours_worked_by_George + 11*hours_worked_by_Jean >= 13)
model.addConstr(8*hours_worked_by_Paul + 11*hours_worked_by_John >= 22)
model.addConstr(2*hours_worked_by_George + 6*hours_worked_by_Ringo >= 12)
model.addConstr(11*hours_worked_by_Bill + 2*hours_worked_by_Hank >= 28)
model.addConstr(11*hours_worked_by_Bill + 2*hours_worked_by_George >= 13)
model.addConstr(2*hours_worked_by_Hank + 6*hours_worked_by_Ringo >= 20)
model.addConstr(6*hours_worked_by_Ringo + 11*hours_worked_by_Jean >= 17)
model.addConstr(8*hours_worked_by_Paul + 2*hours_worked_by_Hank >= 26)
model.addConstr(11*hours_worked_by_John + 6*hours_worked_by_Ringo >= 27)
model.addConstr(8*hours_worked_by_Paul + 11*hours_worked_by_Jean >= 11)
model.addConstr(2*hours_worked_by_George + 2*hours_worked_by_Hank <= 183)
model.addConstr(2*hours_worked_by_George + 6*hours_worked_by_Ringo <= 198)
model.addConstr(11*hours_worked_by_John + 11*hours_worked_by_Jean <= 96)
model.addConstr(6*hours_worked_by_Ringo + 11*hours_worked_by_Jean <= 33)
model.addConstr(11*hours_worked_by_John + 6*hours_worked_by_Ringo <= 167)
model.addConstr(8*hours_worked_by_Paul + 6*hours_worked_by_Ringo <= 71)
model.addConstr(2*hours_worked_by_Hank + 11*hours_worked_by_John <= 64)
model.addConstr(2*hours_worked_by_Hank + 6*hours_worked_by_Ringo <= 52)
model.addConstr(8*hours_worked_by_Paul + 2*hours_worked_by_Hank <= 138)
model.addConstr(8*hours_worked_by_Paul + 2*hours_worked_by_George <= 49)
model.addConstr(11*hours_worked_by_Bill + 2*hours_worked_by_George <= 36)
model.addConstr(11*hours_worked_by_Bill + 2*hours_worked_by_George + 2*hours_worked_by_Hank <= 75)
model.addConstr(2*hours_worked_by_George + 2*hours_worked_by_Hank + 6*hours_worked_by_Ringo <= 165)
model.addConstr(2*hours_worked_by_Hank + 6*hours_worked_by_Ringo + 11*hours_worked_by_Jean <= 205)
model.addConstr(11*hours_worked_by_Bill + 2*hours_worked_by_George + 11*hours_worked_by_John <= 93)
model.addConstr(8*hours_worked_by_Paul + 2*hours_worked_by_Hank + 6*hours_worked_by_Ringo <= 192)
model.addConstr(8*hours_worked_by_Paul + 11*hours_worked_by_Bill + 11*hours_worked_by_Jean <= 101)
model.addConstr(2*hours_worked_by_George + 11*hours_worked_by_John + 11*hours_worked_by_Jean <= 140)
model.addConstr(8*hours_worked_by_Paul + 6*hours_worked_by_Ringo + 11*hours_worked_by_Jean <= 208)
model.addConstr(2*hours_worked_by_Hank + 11*hours_worked_by_John + 11*hours_worked_by_Jean <= 76)
model.addConstr(11*hours_worked_by_Bill + 11*hours_worked_by_John + 11*hours_worked_by_Jean <= 151)
model.addConstr(8*hours_worked_by_Paul + 11*hours_worked_by_Bill + 2*hours_worked_by_George + 
                 2*hours_worked_by_Hank + 11*hours_worked_by_John + 6*hours_worked_by_Ringo + 
                 11*hours_worked_by_Jean <= 151)

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    print("Hours worked by Paul: ", hours_worked_by_Paul.varValue)
    print("Hours worked by Bill: ", hours_worked_by_Bill.varValue)
    print("Hours worked by George: ", hours_worked_by_George.varValue)
    print("Hours worked by Hank: ", hours_worked_by_Hank.varValue)
    print("Hours worked by John: ", hours_worked_by_John.varValue)
    print("Hours worked by Ringo: ", hours_worked_by_Ringo.varValue)
    print("Hours worked by Jean: ", hours_worked_by_Jean.varValue)
else:
    print("The model is infeasible.")
```