## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Ringo', 'hours worked by Hank', 'hours worked by Peggy', 'hours worked by Laura']. Let's denote them as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to minimize is $2.41x_0^2 + 5.49x_0x_1 + 1.74x_0x_2 + 6.27x_0x_3 + 9.86x_1^2 + 1.8x_1x_3 + 4.41x_2^2 + 1.09x_2x_3 + 3.96x_3^2 + 8.0x_0 + 9.94x_1 + 9.96x_2 + 4.91x_3$.

## 3: List the constraints
The constraints are:
- $0.71x_0 \leq 391$
- $0.04x_0 \leq 305$
- $0.32x_1 \leq 391$
- $0.82x_1 \leq 305$
- $0.91x_2 \leq 391$
- $0.66x_2 \leq 305$
- $0.52x_3 \leq 391$
- $0.19x_3 \leq 305$
- $0.91x_2^2 + 0.52x_3^2 \geq 42$
- $0.32x_1 + 0.52x_3 \geq 64$
- $0.71x_0 + 0.32x_1 \geq 67$
- $0.71x_0 + 0.32x_1 + 0.91x_2 + 0.52x_3 \geq 67$
- $0.82x_1 + 0.66x_2 \geq 69$
- $0.04x_0^2 + 0.66x_2^2 \geq 32$
- $0.66x_2 + 0.19x_3 \geq 26$
- $0.04x_0 + 0.19x_3 \geq 40$
- $0.04x_0 + 0.82x_1 + 0.66x_2 + 0.19x_3 \geq 40$
- $x_0 - 6x_2 \geq 0$
- $6x_0 - 10x_3 \geq 0$
- $9x_1^2 - 3x_2^2 + 10x_3^2 \geq 0$
- $0.32x_1 + 0.91x_2 \leq 258$
- $0.71x_0 + 0.52x_3 \leq 321$
- $0.32x_1^2 + 0.52x_3^2 \leq 243$
- $0.32x_1 + 0.91x_2 + 0.52x_3 \leq 154$
- $0.04x_0^2 + 0.19x_3^2 \leq 163$
- $0.66x_2^2 + 0.19x_3^2 \leq 186$
- $0.82x_1 + 0.19x_3 \leq 143$
- $0.04x_0^2 + 0.82x_1^2 + 0.66x_2^2 \leq 245$

## 4: Convert the problem into Gurobi code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="x0", lb=0)  # hours worked by Ringo
x1 = model.addVar(name="x1", lb=0)  # hours worked by Hank
x2 = model.addVar(name="x2", lb=0)  # hours worked by Peggy
x3 = model.addVar(name="x3", lb=0)  # hours worked by Laura

# Define the objective function
model.setObjective(2.41*x0**2 + 5.49*x0*x1 + 1.74*x0*x2 + 6.27*x0*x3 + 
                   9.86*x1**2 + 1.8*x1*x3 + 4.41*x2**2 + 1.09*x2*x3 + 
                   3.96*x3**2 + 8.0*x0 + 9.94*x1 + 9.96*x2 + 4.91*x3, 
                   gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(0.71*x0 <= 391)
model.addConstr(0.04*x0 <= 305)
model.addConstr(0.32*x1 <= 391)
model.addConstr(0.82*x1 <= 305)
model.addConstr(0.91*x2 <= 391)
model.addConstr(0.66*x2 <= 305)
model.addConstr(0.52*x3 <= 391)
model.addConstr(0.19*x3 <= 305)
model.addConstr(0.91*x2**2 + 0.52*x3**2 >= 42)
model.addConstr(0.32*x1 + 0.52*x3 >= 64)
model.addConstr(0.71*x0 + 0.32*x1 >= 67)
model.addConstr(0.71*x0 + 0.32*x1 + 0.91*x2 + 0.52*x3 >= 67)
model.addConstr(0.82*x1 + 0.66*x2 >= 69)
model.addConstr(0.04*x0**2 + 0.66*x2**2 >= 32)
model.addConstr(0.66*x2 + 0.19*x3 >= 26)
model.addConstr(0.04*x0 + 0.19*x3 >= 40)
model.addConstr(0.04*x0 + 0.82*x1 + 0.66*x2 + 0.19*x3 >= 40)
model.addConstr(x0 - 6*x2 >= 0)
model.addConstr(6*x0 - 10*x3 >= 0)
model.addConstr(9*x1**2 - 3*x2**2 + 10*x3**2 >= 0)
model.addConstr(0.32*x1 + 0.91*x2 <= 258)
model.addConstr(0.71*x0 + 0.52*x3 <= 321)
model.addConstr(0.32*x1**2 + 0.52*x3**2 <= 243)
model.addConstr(0.32*x1 + 0.91*x2 + 0.52*x3 <= 154)
model.addConstr(0.04*x0**2 + 0.19*x3**2 <= 163)
model.addConstr(0.66*x2**2 + 0.19*x3**2 <= 186)
model.addConstr(0.82*x1 + 0.19*x3 <= 143)
model.addConstr(0.04*x0**2 + 0.82*x1**2 + 0.66*x2**2 <= 245)

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
else:
    print("The model is infeasible")
```

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Ringo'), 
        ('x1', 'hours worked by Hank'), 
        ('x2', 'hours worked by Peggy'), 
        ('x3', 'hours worked by Laura')
    ], 
    'objective_function': '2.41*x0^2 + 5.49*x0*x1 + 1.74*x0*x2 + 6.27*x0*x3 + 9.86*x1^2 + 1.8*x1*x3 + 4.41*x2^2 + 1.09*x2*x3 + 3.96*x3^2 + 8.0*x0 + 9.94*x1 + 9.96*x2 + 4.91*x3', 
    'constraints': [
        '0.71*x0 <= 391', 
        '0.04*x0 <= 305', 
        '0.32*x1 <= 391', 
        '0.82*x1 <= 305', 
        '0.91*x2 <= 391', 
        '0.66*x2 <= 305', 
        '0.52*x3 <= 391', 
        '0.19*x3 <= 305', 
        '0.91*x2^2 + 0.52*x3^2 >= 42', 
        '0.32*x1 + 0.52*x3 >= 64', 
        '0.71*x0 + 0.32*x1 >= 67', 
        '0.71*x0 + 0.32*x1 + 0.91*x2 + 0.52*x3 >= 67', 
        '0.82*x1 + 0.66*x2 >= 69', 
        '0.04*x0^2 + 0.66*x2^2 >= 32', 
        '0.66*x2 + 0.19*x3 >= 26', 
        '0.04*x0 + 0.19*x3 >= 40', 
        '0.04*x0 + 0.82*x1 + 0.66*x2 + 0.19*x3 >= 40', 
        'x0 - 6*x2 >= 0', 
        '6*x0 - 10*x3 >= 0', 
        '9*x1^2 - 3*x2^2 + 10*x3^2 >= 0', 
        '0.32*x1 + 0.91*x2 <= 258', 
        '0.71*x0 + 0.52*x3 <= 321', 
        '0.32*x1^2 + 0.52*x3^2 <= 243', 
        '0.32*x1 + 0.91*x2 + 0.52*x3 <= 154', 
        '0.04*x0^2 + 0.19*x3^2 <= 163', 
        '0.66*x2^2 + 0.19*x3^2 <= 186', 
        '0.82*x1 + 0.19*x3 <= 143', 
        '0.04*x0^2 + 0.82*x1^2 + 0.66*x2^2 <= 245'
    ]
}
```