## Step 1: Define the symbolic variables and the objective function
The symbolic variables are defined as follows: 
- 'x1' corresponds to 'hours worked by Jean'
- 'x2' corresponds to 'hours worked by Ringo'
- 'x3' corresponds to 'hours worked by John'
- 'x4' corresponds to 'hours worked by George'

The objective function to minimize is: 
\[ 7.35x_1^2 + 9.5x_1x_3 + 5.13x_1x_4 + 5.59x_2^2 + 6.13x_3x_4 + 8.95x_4^2 + 9.56x_1 + 6.49x_2 + 1.6x_3 \]

## Step 2: Define the constraints
The constraints are as follows:
- $7.4x_1 = 7.4$ (Jean's productivity rating)
- $0.29x_1 = 0.29$ (Jean's likelihood to quit index)
- $1.99x_2 = 1.99$ (Ringo's productivity rating)
- $7.73x_2 = 7.73$ (Ringo's likelihood to quit index)
- $2.67x_3 = 2.67$ (John's productivity rating)
- $1.5x_3 = 1.5$ (John's likelihood to quit index)
- $3.4x_4 = 3.4$ (George's productivity rating)
- $2.16x_4 = 2.16$ (George's likelihood to quit index)
- $7.4^2x_1^2 + 3.4^2x_4^2 \geq 23$
- $1.99x_2 + 2.67x_3 \geq 33$
- $7.4^2x_1^2 + 1.99^2x_2^2 \geq 20$
- $7.4^2x_1^2 + 2.67^2x_3^2 \geq 20$
- $7.4x_1 + 1.99x_2 + 2.67x_3 + 3.4x_4 \geq 20$
- $1.5^2x_3^2 + 2.16^2x_4^2 \geq 49$
- $0.29x_1 + 1.5x_3 \geq 36$
- $7.73x_2 + 1.5x_3 \geq 56$
- $7.73x_2 + 2.16x_4 \geq 28$
- $0.29^2x_1^2 + 2.16^2x_4^2 \geq 57$
- $0.29^2x_1^2 + 1.5^2x_3^2 + 2.16^2x_4^2 \geq 50$
- $0.29x_1 + 7.73x_2 + 1.5x_3 + 2.16x_4 \geq 50$
- $7x_2 - 8x_4 \geq 0$
- $3x_1 - 7x_3 \geq 0$
- $7.4^2x_1^2 + 2.67^2x_3^2 + 3.4^2x_4^2 \leq 209$
- $7.73x_2 + 1.5x_3 \leq 206$

## Step 3: Convert the problem into Gurobi code
```python
import gurobi

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

# Define the variables
x1 = m.addVar(name="x1", lb=0)  # hours worked by Jean
x2 = m.addVar(name="x2", lb=0)  # hours worked by Ringo
x3 = m.addVar(name="x3", lb=0)  # hours worked by John
x4 = m.addVar(name="x4", lb=0)  # hours worked by George

# Objective function
m.setObjective(7.35*x1**2 + 9.5*x1*x3 + 5.13*x1*x4 + 5.59*x2**2 + 6.13*x3*x4 + 8.95*x4**2 + 9.56*x1 + 6.49*x2 + 1.6*x3, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(7.4*x1 == 7.4, name="jean_productivity")
m.addConstr(0.29*x1 == 0.29, name="jean_likelihood")
m.addConstr(1.99*x2 == 1.99, name="ringo_productivity")
m.addConstr(7.73*x2 == 7.73, name="ringo_likelihood")
m.addConstr(2.67*x3 == 2.67, name="john_productivity")
m.addConstr(1.5*x3 == 1.5, name="john_likelihood")
m.addConstr(3.4*x4 == 3.4, name="george_productivity")
m.addConstr(2.16*x4 == 2.16, name="george_likelihood")

m.addConstr(7.4**2*x1**2 + 3.4**2*x4**2 >= 23, name="productivity_rating_constraint1")
m.addConstr(1.99*x2 + 2.67*x3 >= 33, name="productivity_rating_constraint2")
m.addConstr(7.4**2*x1**2 + 1.99**2*x2**2 >= 20, name="productivity_rating_constraint3")
m.addConstr(7.4**2*x1**2 + 2.67**2*x3**2 >= 20, name="productivity_rating_constraint4")
m.addConstr(7.4*x1 + 1.99*x2 + 2.67*x3 + 3.4*x4 >= 20, name="productivity_rating_constraint5")

m.addConstr(1.5**2*x3**2 + 2.16**2*x4**2 >= 49, name="likelihood_constraint1")
m.addConstr(0.29*x1 + 1.5*x3 >= 36, name="likelihood_constraint2")
m.addConstr(7.73*x2 + 1.5*x3 >= 56, name="likelihood_constraint3")
m.addConstr(7.73*x2 + 2.16*x4 >= 28, name="likelihood_constraint4")
m.addConstr(0.29**2*x1**2 + 2.16**2*x4**2 >= 57, name="likelihood_constraint5")
m.addConstr(0.29**2*x1**2 + 1.5**2*x3**2 + 2.16**2*x4**2 >= 50, name="likelihood_constraint6")
m.addConstr(0.29*x1 + 7.73*x2 + 1.5*x3 + 2.16*x4 >= 50, name="likelihood_constraint7")

m.addConstr(7*x2 - 8*x4 >= 0, name="hours_worked_constraint1")
m.addConstr(3*x1 - 7*x3 >= 0, name="hours_worked_constraint2")

m.addConstr(7.4**2*x1**2 + 2.67**2*x3**2 + 3.4**2*x4**2 <= 209, name="productivity_rating_constraint6")
m.addConstr(7.73*x2 + 1.5*x3 <= 206, name="likelihood_constraint8")

# Solve the model
m.optimize()

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

## Step 4: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'hours worked by Jean'), 
        ('x2', 'hours worked by Ringo'), 
        ('x3', 'hours worked by John'), 
        ('x4', 'hours worked by George')
    ], 
    'objective_function': '7.35*x1^2 + 9.5*x1*x3 + 5.13*x1*x4 + 5.59*x2^2 + 6.13*x3*x4 + 8.95*x4^2 + 9.56*x1 + 6.49*x2 + 1.6*x3', 
    'constraints': [
        '7.4*x1 = 7.4', 
        '0.29*x1 = 0.29', 
        '1.99*x2 = 1.99', 
        '7.73*x2 = 7.73', 
        '2.67*x3 = 2.67', 
        '1.5*x3 = 1.5', 
        '3.4*x4 = 3.4', 
        '2.16*x4 = 2.16', 
        '7.4^2*x1^2 + 3.4^2*x4^2 >= 23', 
        '1.99*x2 + 2.67*x3 >= 33', 
        '7.4^2*x1^2 + 1.99^2*x2^2 >= 20', 
        '7.4^2*x1^2 + 2.67^2*x3^2 >= 20', 
        '7.4*x1 + 1.99*x2 + 2.67*x3 + 3.4*x4 >= 20', 
        '1.5^2*x3^2 + 2.16^2*x4^2 >= 49', 
        '0.29*x1 + 1.5*x3 >= 36', 
        '7.73*x2 + 1.5*x3 >= 56', 
        '7.73*x2 + 2.16*x4 >= 28', 
        '0.29^2*x1^2 + 2.16^2*x4^2 >= 57', 
        '0.29^2*x1^2 + 1.5^2*x3^2 + 2.16^2*x4^2 >= 50', 
        '0.29*x1 + 7.73*x2 + 1.5*x3 + 2.16*x4 >= 50', 
        '7*x2 - 8*x4 >= 0', 
        '3*x1 - 7*x3 >= 0', 
        '7.4^2*x1^2 + 2.67^2*x3^2 + 3.4^2*x4^2 <= 209', 
        '7.73*x2 + 1.5*x3 <= 206'
    ]
}
```