## Step 1: Define the variables and the objective function
The variables are ['hours worked by Laura', 'hours worked by Dale', 'hours worked by Mary', 'hours worked by Ringo']. Let's denote them as $L$, $D$, $M$, and $R$ respectively. The objective function to maximize is $1L + 2D + 9M + 1R$.

## 2: Define the resources/attributes for each variable
Given resources/attributes:
- $r0$: likelihood to quit index
- $r1$: paperwork competence rating
- $r2$: work quality rating

With specific values for each person:
- Laura: $r0 = 3.13$, $r1 = 5.79$, $r2 = 8.68$
- Dale: $r0 = 5.7$, $r1 = 4.21$, $r2 = 7.47$
- Mary: $r0 = 4.0$, $r1 = 9.35$, $r2 = 1.57$
- Ringo: $r0 = 7.03$, $r1 = 5.22$, $r2 = 5.15$

## 3: Formulate the constraints
1. $3.13L \geq 43$ is not correct, it should be $3.13L + 5.7D \geq 43$
2. $3.13L + 5.7D + 7.03R \geq 28$
3. $8.68L + 7.47D \geq 60$
4. $7.47D + 5.15R \geq 77$
5. $4.0M + 7.03R \leq 166$
6. $3.13L + 5.7D \leq 98$
7. $5.7D + 7.03R \leq 115$
8. $3.13L + 7.03R \leq 190$
9. $5.7D + 4.0M \leq 116$
10. $5.7D + 4.0M + 7.03R \leq 143$
11. $3.13L + 4.0M + 7.03R \leq 67$
12. $3.13L + 5.7D + 4.0M + 7.03R \leq 67$
13. $5.79L + 4.21D \leq 144$
14. $9.35M + 5.22R \leq 120$
15. $5.79L + 5.22R \leq 198$
16. $5.79L + 9.35M + 5.22R \leq 85$
17. $5.79L + 4.21D + 9.35M \leq 146$
18. $4.21D + 9.35M + 5.22R \leq 59$
19. $5.79L + 4.21D + 9.35M + 5.22R \leq 59$
20. $8.68L + 7.47D \leq 84$
21. $1.57M + 5.15R \leq 115$
22. $8.68L + 5.15R \leq 213$
23. $7.47D + 1.57M \leq 114$
24. $7.47D + 5.15R \leq 311$
25. $8.68L + 7.47D + 1.57M \leq 229$
26. $8.68L + 7.47D + 5.15R \leq 221$
27. $8.68L + 1.57M + 5.15R \leq 243$
28. $8.68L + 7.47D + 1.57M + 5.15R \leq 243$

## 4: Implement the problem in Gurobi
```python
import gurobi

def optimize_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    L = model.addVar(lb=0, name="hours_worked_by_Laura")
    D = model.addVar(lb=0, name="hours_worked_by_Dale")
    M = model.addVar(lb=0, name="hours_worked_by_Mary")
    R = model.addVar(lb=0, name="hours_worked_by_Ringo")

    # Define the objective function
    model.setObjective(L + 2 * D + 9 * M + R, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(3.13 * L + 5.7 * D >= 43)
    model.addConstr(3.13 * L + 5.7 * D + 7.03 * R >= 28)
    model.addConstr(8.68 * L + 7.47 * D >= 60)
    model.addConstr(7.47 * D + 5.15 * R >= 77)
    model.addConstr(4.0 * M + 7.03 * R <= 166)
    model.addConstr(3.13 * L + 5.7 * D <= 98)
    model.addConstr(5.7 * D + 7.03 * R <= 115)
    model.addConstr(3.13 * L + 7.03 * R <= 190)
    model.addConstr(5.7 * D + 4.0 * M <= 116)
    model.addConstr(5.7 * D + 4.0 * M + 7.03 * R <= 143)
    model.addConstr(3.13 * L + 4.0 * M + 7.03 * R <= 67)
    model.addConstr(3.13 * L + 5.7 * D + 4.0 * M + 7.03 * R <= 67)
    model.addConstr(5.79 * L + 4.21 * D <= 144)
    model.addConstr(9.35 * M + 5.22 * R <= 120)
    model.addConstr(5.79 * L + 5.22 * R <= 198)
    model.addConstr(5.79 * L + 9.35 * M + 5.22 * R <= 85)
    model.addConstr(5.79 * L + 4.21 * D + 9.35 * M <= 146)
    model.addConstr(4.21 * D + 9.35 * M + 5.22 * R <= 59)
    model.addConstr(5.79 * L + 4.21 * D + 9.35 * M + 5.22 * R <= 59)
    model.addConstr(8.68 * L + 7.47 * D <= 84)
    model.addConstr(1.57 * M + 5.15 * R <= 115)
    model.addConstr(8.68 * L + 5.15 * R <= 213)
    model.addConstr(7.47 * D + 1.57 * M <= 114)
    model.addConstr(7.47 * D + 5.15 * R <= 311)
    model.addConstr(8.68 * L + 7.47 * D + 1.57 * M <= 229)
    model.addConstr(8.68 * L + 7.47 * D + 5.15 * R <= 221)
    model.addConstr(8.68 * L + 1.57 * M + 5.15 * R <= 243)
    model.addConstr(8.68 * L + 7.47 * D + 1.57 * M + 5.15 * R <= 243)

    # Solve the problem
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Laura: ", L.varValue)
        print("Hours worked by Dale: ", D.varValue)
        print("Hours worked by Mary: ", M.varValue)
        print("Hours worked by Ringo: ", R.varValue)
    else:
        print("The problem is infeasible")

optimize_problem()
```