## Step 1: Define the variables and the objective function
The variables are 'hours worked by Hank', 'hours worked by Bill', 'hours worked by Laura', and 'hours worked by Jean'. Let's denote them as $H$, $B$, $L$, and $J$ respectively. The objective function to maximize is $4.7H^2 + 1.48HB + 8.34HJ + 9.02B^2 + 1.32BJ + 5.27B$.

## 2: Define the constraints
1. $H \cdot 4 = 4$ (Hank's computer competence rating is 4, but this seems to be an equality constraint which might be misinterpreted. Assuming it's about the rating being a constant factor, we actually have $x0=4$ as a given attribute, not a constraint in the traditional sense),
2. $B \cdot 9 = 9$ (similarly for Bill),
3. $L \cdot 3 = 3$ (for Laura),
4. $J \cdot 6 = 6$ (for Jean).
However, these seem more like given attributes:
- $x0 = 4$, $x1 = 9$, $x2 = 3$, $x3 = 6$ for $H$, $B$, $L$, $J$ respectively.

Given constraints:
- $H^2 + B^2 + J^2 \geq 28$,
- $B + L + J \geq 28$,
- $H + B + J \geq 21$,
- $B + L + J \geq 21$,
- $L + J \leq 79$,
- $H + L \leq 159$,
- $H^2 + J^2 \leq 63$,
- $H^2 + B^2 \leq 45$,
- $B \cdot J \leq 145$,
- $H + B + L \leq 70$,
- $H + L + J \leq 133$,
- $H + B + L + J \leq 133$.

## 3: Formulate the problem in Gurobi
We will use Gurobi to solve this optimization problem. The problem is a nonlinear programming problem due to the quadratic terms in the objective function and some constraints.

```python
import gurobi as gp

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

# Define the variables
H = m.addVar(lb=-gp.GRB.INFINITY, name="hours_worked_by_Hank")
B = m.addVar(lb=-gp.GRB.INFINITY, name="hours_worked_by_Bill")
L = m.addVar(lb=-gp.GRB.INFINITY, name="hours_worked_by_Laura")
J = m.addVar(lb=-gp.GRB.INFINITY, name="hours_worked_by_Jean")

# Objective function
m.setObjective(4.7 * H**2 + 1.48 * H * B + 8.34 * H * J + 9.02 * B**2 + 1.32 * B * J + 5.27 * B, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(H * 4 <= 161, "Hank_computer_competence")
m.addConstr(B * 9 <= 161, "Bill_computer_competence")
m.addConstr(L * 3 <= 161, "Laura_computer_competence")
m.addConstr(J * 6 <= 161, "Jean_computer_competence")

m.addConstr(H**2 + B**2 + J**2 >= 28, "total_computer_competence_rating_squared")
m.addConstr(B + L + J >= 28, "total_B_L_J_computer_competence")
m.addConstr(H + B + J >= 21, "total_H_B_J_computer_competence")
m.addConstr(B + L + J >= 21, "total_B_L_J_computer_competence_alternate")
m.addConstr(L + J <= 79, "L_J_computer_competence_max")
m.addConstr(H + L <= 159, "H_L_computer_competence_max")
m.addConstr(H**2 + J**2 <= 63, "H_J_computer_competence_squared_max")
m.addConstr(H**2 + B**2 <= 45, "H_B_computer_competence_squared_max")
m.addConstr(B * J <= 145, "B_J_computer_competence_max")
m.addConstr(H + B + L <= 70, "H_B_L_computer_competence_max")
m.addConstr(H + L + J <= 133, "H_L_J_computer_competence_max")
m.addConstr(H + B + L + J <= 133, "total_computer_competence_max")

# Solve the problem
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("H: ", H.varValue)
    print("B: ", B.varValue)
    print("L: ", L.varValue)
    print("J: ", J.varValue)
else:
    print("The problem is infeasible")
```