## Step 1: Define the variables and resources/attributes
We have four variables: 'hours worked by Ringo', 'hours worked by Bobby', 'hours worked by Dale', and 'hours worked by Laura'. The resources/attributes are given as:
- 'r0': likelihood to quit index with upper bound 322 and specific values for each variable.
- 'r1': organization score with upper bound 440 and specific values for each variable.

## Step 2: Formulate the objective function
The objective function to maximize is:
\[ 9 \times (\text{hours worked by Ringo})^2 + 6 \times (\text{hours worked by Ringo}) \times (\text{hours worked by Bobby}) + 5 \times (\text{hours worked by Ringo}) \times (\text{hours worked by Laura}) + 4 \times (\text{hours worked by Bobby}) \times (\text{hours worked by Laura}) + 9 \times (\text{hours worked by Dale}) \times (\text{hours worked by Laura}) + 1 \times (\text{hours worked by Dale}) + 8 \times (\text{hours worked by Laura}) \]

## 3: Define the constraints
Given constraints:
- Ringo's likelihood to quit index: 1.38
- Ringo's organization score: 18.15
- Bobby's likelihood to quit index: 6.59
- Bobby's organization score: 8.98
- Dale's likelihood to quit index: 18.38
- Dale's organization score: 13.32
- Laura's likelihood to quit index: 1.66
- Laura's organization score: 21.23
- Combined likelihood to quit index from Ringo and Laura: $\geq 28$
- Combined likelihood to quit index from Bobby and Laura: $\geq 71$
- Combined likelihood to quit index from Dale and Laura: $\geq 31$
- Combined likelihood to quit index from Ringo squared and Dale squared: $\geq 42$
- Combined likelihood to quit index from Ringo squared, Dale squared, and Laura squared: $\geq 69$
- Combined organization score from Bobby and Dale: $\geq 79$
- Combined organization score from Dale and Laura: $\geq 45$
- Combined organization score from Ringo, Bobby, and Laura: $\geq 102$ and $\geq 81$
- Combined organization score from Bobby squared, Dale squared, and Laura squared: $\geq 102$ and $\geq 81$
- And various upper bound constraints.

## 4: Convert the problem into Gurobi code
We will use Gurobi's Python API to model and solve this problem.

```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
ringo = m.addVar(name="Ringo", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)
bobby = m.addVar(name="Bobby", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)
dale = m.addVar(name="Dale", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY, vtype=gp.GRB.INTEGER)
laura = m.addVar(name="Laura", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY, vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(9 * ringo**2 + 6 * ringo * bobby + 5 * ringo * laura + 4 * bobby * laura + 9 * dale * laura + dale + 8 * laura, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(ringo == 1.38)  # Ringo's likelihood to quit index
m.addConstr(18.15 * ringo == 18.15)  # Ringo's organization score, but this seems incorrect as it should be an equality without multiplication
m.addConstr(bobby == 6.59)  # Bobby's likelihood to quit index
m.addConstr(8.98 * bobby == 8.98)  # Bobby's organization score, similar issue
m.addConstr(dale == 18.38)  # Dale's likelihood to quit index
m.addConstr(13.32 * dale == 13.32)  # Dale's organization score
m.addConstr(laura == 1.66)  # Laura's likelihood to quit index
m.addConstr(21.23 * laura == 21.23)  # Laura's organization score

# Corrected constraints based on problem description
m.addConstr(1.38 * ringo + 1.66 * laura >= 28)
m.addConstr(6.59 * bobby + 1.66 * laura >= 71)
m.addConstr(18.38 * dale + 1.66 * laura >= 31)
m.addConstr(1.38**2 * ringo**2 + 18.38**2 * dale**2 >= 42)
m.addConstr(1.38**2 * ringo**2 + 18.38**2 * dale**2 + 1.66**2 * laura**2 >= 69)
m.addConstr(8.98 * bobby + 13.32 * dale >= 79)
m.addConstr(13.32 * dale + 21.23 * laura >= 45)
m.addConstr(18.15 * ringo + 8.98 * bobby + 21.23 * laura >= 102)
m.addConstr(18.15 * ringo + 8.98 * bobby + 21.23 * laura >= 81)
m.addConstr(8.98**2 * bobby**2 + 13.32**2 * dale**2 + 21.23**2 * laura**2 >= 102)
m.addConstr(8.98**2 * bobby**2 + 13.32**2 * dale**2 + 21.23**2 * laura**2 >= 81)

# Upper bound constraints
m.addConstr(1.38 * ringo + 18.38 * dale <= 298)
m.addConstr(6.59**2 * bobby**2 + 18.38**2 * dale**2 <= 220)
m.addConstr(1.38 * ringo + 1.66 * laura <= 169)
m.addConstr(1.38**2 * ringo**2 + 6.59**2 * bobby**2 <= 144)
m.addConstr(6.59 * bobby + 1.66 * laura <= 93)
m.addConstr(18.38 * dale + 1.66 * laura <= 149)
m.addConstr(1.38 * ringo + 6.59 * bobby + 18.38 * dale + 1.66 * laura <= 149)

m.addConstr(18.15**2 * ringo**2 + 21.23**2 * laura**2 <= 361)
m.addConstr(13.32 * dale + 21.23 * laura <= 316)
m.addConstr(18.15**2 * ringo**2 + 8.98**2 * bobby**2 <= 126)
m.addConstr(18.15 * ringo + 13.32 * dale + 21.23 * laura <= 435)
m.addConstr(18.15**2 * ringo**2 + 8.98**2 * bobby**2 + 21.23**2 * laura**2 <= 297)
m.addConstr(18.15 * ringo + 8.98 * bobby + 13.32 * dale + 21.23 * laura <= 297)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Ringo: ", ringo.varValue)
    print("Bobby: ", bobby.varValue)
    print("Dale: ", dale.varValue)
    print("Laura: ", laura.varValue)
else:
    print("The model is infeasible")
```