## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Hank', 'hours worked by Bill', 'hours worked by Laura', 'hours worked by Jean'] which can be represented symbolically as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_1$ : hours worked by Hank
- $x_2$ : hours worked by Bill
- $x_3$ : hours worked by Laura
- $x_4$ : hours worked by Jean

## 3: Define the objective function in symbolic notation
The objective function to maximize is: $4.7x_1^2 + 1.48x_1x_2 + 8.34x_1x_4 + 9.02x_2^2 + 1.32x_2x_4 + 5.27x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $4x_1 \leq 161$ (Hank's computer competence rating is 4, but this seems to be an upper bound on $x_1$ times 4, not a direct constraint on $x_1$)
- $9x_2 \leq 161$ (Bill's computer competence rating is 9, similar to Hank's)
- $3x_3 \leq 161$ (Laura's computer competence rating is 3)
- $6x_4 \leq 161$ (Jean's computer competence rating is 6)
- $4^2x_1^2 + 9^2x_2^2 + 6^2x_4^2 \geq 28$ (total combined computer competence rating from hours worked by Hank, Bill, and Jean squared)
- $9x_2 + 3x_3 + 6x_4 \geq 28$ (total combined computer competence rating from hours worked by Bill, Laura, and Jean)
- $4x_1 + 9x_2 + 6x_4 \geq 21$ (total combined computer competence rating from hours worked by Hank, Bill, and Jean)
- $9x_2 + 3x_3 + 6x_4 \geq 21$ (similar to the previous one but with Laura included)
- $3x_3 + 6x_4 \leq 79$ (total combined computer competence rating from hours worked by Laura and Jean)
- $4x_1 + 3x_3 \leq 159$ (total combined computer competence rating from hours worked by Hank and Laura)
- $4^2x_1^2 + 6^2x_4^2 \leq 63$ (total combined computer competence rating from hours worked by Hank and Jean squared)
- $4^2x_1^2 + 9^2x_2^2 \leq 45$ (total combined computer competence rating from hours worked by Hank and Bill squared)
- $9x_2 + 6x_4 \leq 145$ (total combined computer competence rating from hours worked by Bill and Jean)
- $4x_1 + 9x_2 + 3x_3 \leq 70$ (total combined computer competence rating from hours worked by Hank, Bill, and Laura)
- $4x_1 + 3x_3 + 6x_4 \leq 133$ (total combined computer competence rating from hours worked by Hank, Laura, and Jean)
- $4x_1 + 9x_2 + 3x_3 + 6x_4 \leq 133$ (total combined computer competence rating from all)

## 5: Correct and simplify constraints based on given attributes
Given attributes:
- $x_0 = 4$ for Hank
- $x_1 = 9$ for Bill
- $x_2 = 3$ for Laura
- $x_3 = 6$ for Jean

And resource $r0$ with an upper bound of 161.

## 6: Formulate the problem in Gurobi
We need to maximize $4.7x_1^2 + 1.48x_1x_2 + 8.34x_1x_4 + 9.02x_2^2 + 1.32x_2x_4 + 5.27x_2$ subject to the constraints.

## 7: Write the Gurobi code
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name="x1", lb=-gurobi.GRB.INFINITY)  # hours worked by Hank
x2 = m.addVar(name="x2", lb=-gurobi.GRB.INFINITY)  # hours worked by Bill
x3 = m.addVar(name="x3", lb=-gurobi.GRB.INFINITY)  # hours worked by Laura
x4 = m.addVar(name="x4", lb=-gurobi.GRB.INFINITY)  # hours worked by Jean

# Objective function
m.setObjective(4.7*x1**2 + 1.48*x1*x2 + 8.34*x1*x4 + 9.02*x2**2 + 1.32*x2*x4 + 5.27*x2, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(4*x1 <= 161)
m.addConstr(9*x2 <= 161)
m.addConstr(3*x3 <= 161)
m.addConstr(6*x4 <= 161)

m.addConstr(16*x1**2 + 81*x2**2 + 36*x4**2 >= 28)
m.addConstr(9*x2 + 3*x3 + 6*x4 >= 28)
m.addConstr(4*x1 + 9*x2 + 6*x4 >= 21)
m.addConstr(9*x2 + 3*x3 + 6*x4 >= 21)
m.addConstr(3*x3 + 6*x4 <= 79)
m.addConstr(4*x1 + 3*x3 <= 159)
m.addConstr(16*x1**2 + 36*x4**2 <= 63)
m.addConstr(16*x1**2 + 81*x2**2 <= 45)
m.addConstr(9*x2 + 6*x4 <= 145)
m.addConstr(4*x1 + 9*x2 + 3*x3 <= 70)
m.addConstr(4*x1 + 3*x3 + 6*x4 <= 133)
m.addConstr(4*x1 + 9*x2 + 3*x3 + 6*x4 <= 133)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
    print("x4: ", x4.varValue)
else:
    print("The model is infeasible")
```

## 8: Symbolic representation
```json
{
    'sym_variables': [('x1', 'hours worked by Hank'), ('x2', 'hours worked by Bill'), ('x3', 'hours worked by Laura'), ('x4', 'hours worked by Jean')],
    'objective_function': '4.7*x1^2 + 1.48*x1*x2 + 8.34*x1*x4 + 9.02*x2^2 + 1.32*x2*x4 + 5.27*x2',
    'constraints': [
        '4*x1 <= 161',
        '9*x2 <= 161',
        '3*x3 <= 161',
        '6*x4 <= 161',
        '16*x1^2 + 81*x2^2 + 36*x4^2 >= 28',
        '9*x2 + 3*x3 + 6*x4 >= 28',
        '4*x1 + 9*x2 + 6*x4 >= 21',
        '9*x2 + 3*x3 + 6*x4 >= 21',
        '3*x3 + 6*x4 <= 79',
        '4*x1 + 3*x3 <= 159',
        '16*x1^2 + 36*x4^2 <= 63',
        '16*x1^2 + 81*x2^2 <= 45',
        '9*x2 + 6*x4 <= 145',
        '4*x1 + 9*x2 + 3*x3 <= 70',
        '4*x1 + 3*x3 + 6*x4 <= 133',
        '4*x1 + 9*x2 + 3*x3 + 6*x4 <= 133'
    ]
}
```