## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Ringo', 'hours worked by Bobby', 'hours worked by Hank', 'hours worked by Mary']. 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 maximize is $6.1x_0 + 8.29x_1 + 4.21x_2 + 2.36x_3$.

## Step 3: List all the constraints
The constraints are:
- $11x_0 \leq 210$
- $3x_0 \leq 106$
- $4x_0 \leq 112$
- $2x_0 \leq 54$
- $8x_1 \leq 210$
- $6x_1 \leq 106$
- $10x_1 \leq 112$
- $8x_1 \leq 54$
- $7x_2 \leq 210$
- $9x_2 \leq 106$
- $3x_2 \leq 112$
- $8x_2 \leq 54$
- $3x_3 \leq 210$
- $4x_3 \leq 106$
- $7x_3 \leq 112$
- $11x_3 \leq 54$
- $11x_0 + 8x_1 + 7x_2 \geq 39$
- $11x_0 + 8x_1 + 3x_3 \geq 39$
- $11x_0 + 8x_1 + 7x_2 \geq 47$
- $11x_0 + 8x_1 + 3x_3 \geq 47$
- $3x_0 + 4x_3 \geq 8$
- $9x_2 + 4x_3 \geq 15$
- $6x_1 + 9x_2 \geq 18$
- $3x_0 + 6x_1 + 4x_3 \geq 21$
- $3x_2 + 7x_3 \geq 20$
- $10x_1 + 7x_3 \geq 11$
- $4x_0 + 3x_2 \geq 25$
- $10x_1 + 3x_2 \geq 21$
- $4x_0 + 7x_3 \geq 28$
- $4x_0 + 3x_2 + 7x_3 \geq 20$
- $2x_0 + 8x_2 \geq 6$
- $11x_0 + 3x_3 \leq 195$
- $11x_0 + 7x_2 \leq 169$
- $11x_0 + 8x_1 \leq 72$
- $8x_1 + 7x_2 \leq 128$
- $11x_0 + 8x_1 + 3x_3 \leq 74$
- $11x_0 + 8x_1 + 7x_2 \leq 193$
- $11x_0 + 8x_1 + 7x_2 + 3x_3 \leq 193$
- $3x_0 + 9x_2 \leq 57$
- $3x_0 + 6x_1 \leq 103$
- $3x_0 + 6x_1 + 9x_2 + 4x_3 \leq 103$
- $4x_0 + 3x_2 \leq 87$
- $10x_1 + 7x_3 \leq 106$
- $3x_2 + 7x_3 \leq 45$
- $4x_0 + 10x_1 + 3x_2 \leq 79$
- $10x_1 + 3x_2 + 7x_3 \leq 73$
- $4x_0 + 10x_1 + 7x_3 \leq 43$
- $4x_0 + 10x_1 + 3x_2 + 7x_3 \leq 43$
- $8x_2 + 11x_3 \leq 46$
- $2x_0 + 11x_3 \leq 21$
- $8x_1 + 8x_2 + 11x_3 \leq 24$
- $2x_0 + 8x_1 + 8x_2 + 11x_3 \leq 24$
- $x_0$ is an integer.

## 4: Write down the gurobi code
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name='x0', lb=0, ub=None, vtype=gurobi.GRB.INTEGER)  # hours worked by Ringo
x1 = m.addVar(name='x1', lb=0, ub=None)  # hours worked by Bobby
x2 = m.addVar(name='x2', lb=0, ub=None)  # hours worked by Hank
x3 = m.addVar(name='x3', lb=0, ub=None)  # hours worked by Mary

# Define the objective function
m.setObjective(6.1*x0 + 8.29*x1 + 4.21*x2 + 2.36*x3, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(11*x0 <= 210)
m.addConstr(3*x0 <= 106)
m.addConstr(4*x0 <= 112)
m.addConstr(2*x0 <= 54)
m.addConstr(8*x1 <= 210)
m.addConstr(6*x1 <= 106)
m.addConstr(10*x1 <= 112)
m.addConstr(8*x1 <= 54)
m.addConstr(7*x2 <= 210)
m.addConstr(9*x2 <= 106)
m.addConstr(3*x2 <= 112)
m.addConstr(8*x2 <= 54)
m.addConstr(3*x3 <= 210)
m.addConstr(4*x3 <= 106)
m.addConstr(7*x3 <= 112)
m.addConstr(11*x3 <= 54)
m.addConstr(11*x0 + 8*x1 + 7*x2 >= 39)
m.addConstr(11*x0 + 8*x1 + 3*x3 >= 39)
m.addConstr(11*x0 + 8*x1 + 7*x2 >= 47)
m.addConstr(11*x0 + 8*x1 + 3*x3 >= 47)
m.addConstr(3*x0 + 4*x3 >= 8)
m.addConstr(9*x2 + 4*x3 >= 15)
m.addConstr(6*x1 + 9*x2 >= 18)
m.addConstr(3*x0 + 6*x1 + 4*x3 >= 21)
m.addConstr(3*x2 + 7*x3 >= 20)
m.addConstr(10*x1 + 7*x3 >= 11)
m.addConstr(4*x0 + 3*x2 >= 25)
m.addConstr(10*x1 + 3*x2 >= 21)
m.addConstr(4*x0 + 7*x3 >= 28)
m.addConstr(4*x0 + 3*x2 + 7*x3 >= 20)
m.addConstr(2*x0 + 8*x2 >= 6)
m.addConstr(11*x0 + 3*x3 <= 195)
m.addConstr(11*x0 + 7*x2 <= 169)
m.addConstr(11*x0 + 8*x1 <= 72)
m.addConstr(8*x1 + 7*x2 <= 128)
m.addConstr(11*x0 + 8*x1 + 3*x3 <= 74)
m.addConstr(11*x0 + 8*x1 + 7*x2 <= 193)
m.addConstr(11*x0 + 8*x1 + 7*x2 + 3*x3 <= 193)
m.addConstr(3*x0 + 9*x2 <= 57)
m.addConstr(3*x0 + 6*x1 <= 103)
m.addConstr(3*x0 + 6*x1 + 9*x2 + 4*x3 <= 103)
m.addConstr(4*x0 + 3*x2 <= 87)
m.addConstr(10*x1 + 7*x3 <= 106)
m.addConstr(3*x2 + 7*x3 <= 45)
m.addConstr(4*x0 + 10*x1 + 3*x2 <= 79)
m.addConstr(10*x1 + 3*x2 + 7*x3 <= 73)
m.addConstr(4*x0 + 10*x1 + 7*x3 <= 43)
m.addConstr(4*x0 + 10*x1 + 3*x2 + 7*x3 <= 43)
m.addConstr(8*x2 + 11*x3 <= 46)
m.addConstr(2*x0 + 11*x3 <= 21)
m.addConstr(8*x1 + 8*x2 + 11*x3 <= 24)
m.addConstr(2*x0 + 8*x1 + 8*x2 + 11*x3 <= 24)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('x0: ', x0.varValue)
    print('x1: ', x1.varValue)
    print('x2: ', x2.varValue)
    print('x3: ', x3.varValue)
else:
    print('No solution found')
```

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Ringo'),
        ('x1', 'hours worked by Bobby'),
        ('x2', 'hours worked by Hank'),
        ('x3', 'hours worked by Mary')
    ],
    'objective_function': '6.1*x0 + 8.29*x1 + 4.21*x2 + 2.36*x3',
    'constraints': [
        '11*x0 <= 210',
        '3*x0 <= 106',
        '4*x0 <= 112',
        '2*x0 <= 54',
        '8*x1 <= 210',
        '6*x1 <= 106',
        '10*x1 <= 112',
        '8*x1 <= 54',
        '7*x2 <= 210',
        '9*x2 <= 106',
        '3*x2 <= 112',
        '8*x2 <= 54',
        '3*x3 <= 210',
        '4*x3 <= 106',
        '7*x3 <= 112',
        '11*x3 <= 54',
        '11*x0 + 8*x1 + 7*x2 >= 39',
        '11*x0 + 8*x1 + 3*x3 >= 39',
        '11*x0 + 8*x1 + 7*x2 >= 47',
        '11*x0 + 8*x1 + 3*x3 >= 47',
        '3*x0 + 4*x3 >= 8',
        '9*x2 + 4*x3 >= 15',
        '6*x1 + 9*x2 >= 18',
        '3*x0 + 6*x1 + 4*x3 >= 21',
        '3*x2 + 7*x3 >= 20',
        '10*x1 + 7*x3 >= 11',
        '4*x0 + 3*x2 >= 25',
        '10*x1 + 3*x2 >= 21',
        '4*x0 + 7*x3 >= 28',
        '4*x0 + 3*x2 + 7*x3 >= 20',
        '2*x0 + 8*x2 >= 6',
        '11*x0 + 3*x3 <= 195',
        '11*x0 + 7*x2 <= 169',
        '11*x0 + 8*x1 <= 72',
        '8*x1 + 7*x2 <= 128',
        '11*x0 + 8*x1 + 3*x3 <= 74',
        '11*x0 + 8*x1 + 7*x2 <= 193',
        '11*x0 + 8*x1 + 7*x2 + 3*x3 <= 193',
        '3*x0 + 9*x2 <= 57',
        '3*x0 + 6*x1 <= 103',
        '3*x0 + 6*x1 + 9*x2 + 4*x3 <= 103',
        '4*x0 + 3*x2 <= 87',
        '10*x1 + 7*x3 <= 106',
        '3*x2 + 7*x3 <= 45',
        '4*x0 + 10*x1 + 3*x2 <= 79',
        '10*x1 + 3*x2 + 7*x3 <= 73',
        '4*x0 + 10*x1 + 7*x3 <= 43',
        '4*x0 + 10*x1 + 3*x2 + 7*x3 <= 43',
        '8*x2 + 11*x3 <= 46',
        '2*x0 + 11*x3 <= 21',
        '8*x1 + 8*x2 + 11*x3 <= 24',
        '2*x0 + 8*x1 + 8*x2 + 11*x3 <= 24'
    ]
}
```