## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Hank', 'hours worked by Ringo', 'hours worked by John', '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 $5.51x_0 + 6.01x_1 + 3.55x_2 + 3.47x_3$.

## Step 3: List all the constraints
The constraints are:
- $2x_0 \leq 152$
- $14x_0 \leq 196$
- $6x_0 \leq 194$
- $11x_1 \leq 152$
- $8x_1 \leq 196$
- $13x_1 \leq 194$
- $15x_2 \leq 152$
- $1x_2 \leq 196$
- $14x_2 \leq 194$
- $17x_3 \leq 152$
- $23x_3 \leq 196$
- $23x_3 \leq 194$
- $2x_0 + 11x_1 \geq 33$
- $15x_2 + 17x_3 \geq 21$
- $11x_1 + 17x_3 \geq 18$
- $2x_0 + 11x_1 + 17x_3 \geq 29$
- $2x_0 + 11x_1 + 15x_2 \geq 29$
- $11x_1 + 15x_2 + 17x_3 \geq 29$
- $2x_0 + 11x_1 + 17x_3 \geq 24$
- $2x_0 + 11x_1 + 15x_2 \geq 24$
- $11x_1 + 15x_2 + 17x_3 \geq 24$
- $2x_0 + 11x_1 + 17x_3 \geq 21$
- $2x_0 + 11x_1 + 15x_2 \geq 21$
- $11x_1 + 15x_2 + 17x_3 \geq 21$
- $8x_1 + 1x_2 + 23x_3 \geq 28$
- $13x_1 + 14x_2 \geq 18$
- $6x_0 + 23x_3 \geq 29$
- $14x_2 + 23x_3 \geq 32$
- $6x_0 + 14x_2 + 23x_3 \geq 36$
- $2x_0 + 11x_1 \leq 83$
- $15x_2 + 17x_3 \leq 86$
- $2x_0 + 15x_2 \leq 147$
- $11x_1 + 17x_3 \leq 50$
- $2x_0 + 17x_3 \leq 67$
- $2x_0 + 11x_1 + 15x_2 + 17x_3 \leq 67$
- $8x_1 + 1x_2 \leq 185$
- $1x_2 + 23x_3 \leq 85$
- $8x_1 + 23x_3 \leq 185$
- $14x_0 + 1x_2 \leq 142$
- $14x_0 + 8x_1 \leq 159$
- $14x_0 + 8x_1 + 1x_2 + 23x_3 \leq 159$
- $14x_2 + 23x_3 \leq 71$
- $6x_0 + 23x_3 \leq 178$
- $6x_0 + 14x_2 \leq 187$
- $13x_1 + 23x_3 \leq 136$
- $6x_0 + 13x_1 \leq 93$
- $13x_1 + 14x_2 + 23x_3 \leq 127$
- $6x_0 + 13x_1 + 14x_2 \leq 121$
- $6x_0 + 13x_1 + 23x_3 \leq 58$
- $6x_0 + 13x_1 + 14x_2 + 23x_3 \leq 58$

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

# Define the model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="x0", lb=0)  # hours worked by Hank
x1 = m.addVar(name="x1", lb=0)  # hours worked by Ringo
x2 = m.addVar(name="x2", lb=0)  # hours worked by John
x3 = m.addVar(name="x3", lb=0)  # hours worked by Mary

# Define the objective function
m.setObjective(5.51 * x0 + 6.01 * x1 + 3.55 * x2 + 3.47 * x3, gurobi.GRB.MAXIMIZE)

# Add constraints
# Individual ratings
m.addConstr(2 * x0 <= 152)
m.addConstr(14 * x0 <= 196)
m.addConstr(6 * x0 <= 194)
m.addConstr(11 * x1 <= 152)
m.addConstr(8 * x1 <= 196)
m.addConstr(13 * x1 <= 194)
m.addConstr(15 * x2 <= 152)
m.addConstr(x2 <= 196)
m.addConstr(14 * x2 <= 194)
m.addConstr(17 * x3 <= 152)
m.addConstr(23 * x3 <= 196)
m.addConstr(23 * x3 <= 194)

# Combined ratings
m.addConstr(2 * x0 + 11 * x1 >= 33)
m.addConstr(15 * x2 + 17 * x3 >= 21)
m.addConstr(11 * x1 + 17 * x3 >= 18)
m.addConstr(2 * x0 + 11 * x1 + 17 * x3 >= 29)
m.addConstr(2 * x0 + 11 * x1 + 15 * x2 >= 29)
m.addConstr(11 * x1 + 15 * x2 + 17 * x3 >= 29)
m.addConstr(2 * x0 + 11 * x1 + 17 * x3 >= 24)
m.addConstr(2 * x0 + 11 * x1 + 15 * x2 >= 24)
m.addConstr(11 * x1 + 15 * x2 + 17 * x3 >= 24)
m.addConstr(2 * x0 + 11 * x1 + 17 * x3 >= 21)
m.addConstr(2 * x0 + 11 * x1 + 15 * x2 >= 21)
m.addConstr(11 * x1 + 15 * x2 + 17 * x3 >= 21)
m.addConstr(8 * x1 + x2 + 23 * x3 >= 28)
m.addConstr(13 * x1 + 14 * x2 >= 18)
m.addConstr(6 * x0 + 23 * x3 >= 29)
m.addConstr(14 * x2 + 23 * x3 >= 32)
m.addConstr(6 * x0 + 14 * x2 + 23 * x3 >= 36)

# Upper bounds for combined ratings
m.addConstr(2 * x0 + 11 * x1 <= 83)
m.addConstr(15 * x2 + 17 * x3 <= 86)
m.addConstr(2 * x0 + 15 * x2 <= 147)
m.addConstr(11 * x1 + 17 * x3 <= 50)
m.addConstr(2 * x0 + 17 * x3 <= 67)
m.addConstr(2 * x0 + 11 * x1 + 15 * x2 + 17 * x3 <= 67)
m.addConstr(8 * x1 + x2 <= 185)
m.addConstr(x2 + 23 * x3 <= 85)
m.addConstr(8 * x1 + 23 * x3 <= 185)
m.addConstr(14 * x0 + x2 <= 142)
m.addConstr(14 * x0 + 8 * x1 <= 159)
m.addConstr(14 * x0 + 8 * x1 + x2 + 23 * x3 <= 159)
m.addConstr(14 * x2 + 23 * x3 <= 71)
m.addConstr(6 * x0 + 23 * x3 <= 178)
m.addConstr(6 * x0 + 14 * x2 <= 187)
m.addConstr(13 * x1 + 23 * x3 <= 136)
m.addConstr(6 * x0 + 13 * x1 <= 93)
m.addConstr(13 * x1 + 14 * x2 + 23 * x3 <= 127)
m.addConstr(6 * x0 + 13 * x1 + 14 * x2 <= 121)
m.addConstr(6 * x0 + 13 * x1 + 23 * x3 <= 58)
m.addConstr(6 * x0 + 13 * x1 + 14 * x2 + 23 * x3 <= 58)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("Hours worked by Hank: ", x0.varValue)
    print("Hours worked by Ringo: ", x1.varValue)
    print("Hours worked by John: ", x2.varValue)
    print("Hours worked by Mary: ", x3.varValue)
else:
    print("No optimal solution found")
```

## Step 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Hank'), 
        ('x1', 'hours worked by Ringo'), 
        ('x2', 'hours worked by John'), 
        ('x3', 'hours worked by Mary')
    ], 
    'objective_function': '5.51*x0 + 6.01*x1 + 3.55*x2 + 3.47*x3', 
    'constraints': [
        '2*x0 <= 152', '14*x0 <= 196', '6*x0 <= 194', 
        '11*x1 <= 152', '8*x1 <= 196', '13*x1 <= 194', 
        '15*x2 <= 152', 'x2 <= 196', '14*x2 <= 194', 
        '17*x3 <= 152', '23*x3 <= 196', '23*x3 <= 194', 
        '2*x0 + 11*x1 >= 33', '15*x2 + 17*x3 >= 21', 
        '11*x1 + 17*x3 >= 18', '2*x0 + 11*x1 + 17*x3 >= 29', 
        '2*x0 + 11*x1 + 15*x2 >= 29', '11*x1 + 15*x2 + 17*x3 >= 29', 
        '2*x0 + 11*x1 + 17*x3 >= 24', '2*x0 + 11*x1 + 15*x2 >= 24', 
        '11*x1 + 15*x2 + 17*x3 >= 24', '2*x0 + 11*x1 + 17*x3 >= 21', 
        '2*x0 + 11*x1 + 15*x2 >= 21', '11*x1 + 15*x2 + 17*x3 >= 21', 
        '8*x1 + x2 + 23*x3 >= 28', '13*x1 + 14*x2 >= 18', 
        '6*x0 + 23*x3 >= 29', '14*x2 + 23*x3 >= 32', 
        '6*x0 + 14*x2 + 23*x3 >= 36', '2*x0 + 11*x1 <= 83', 
        '15*x2 + 17*x3 <= 86', '2*x0 + 15*x2 <= 147', 
        '11*x1 + 17*x3 <= 50', '2*x0 + 17*x3 <= 67', 
        '2*x0 + 11*x1 + 15*x2 + 17*x3 <= 67', '8*x1 + x2 <= 185', 
        'x2 + 23*x3 <= 85', '8*x1 + 23*x3 <= 185', 
        '14*x0 + x2 <= 142', '14*x0 + 8*x1 <= 159', 
        '14*x0 + 8*x1 + x2 + 23*x3 <= 159', '14*x2 + 23*x3 <= 71', 
        '6*x0 + 23*x3 <= 178', '6*x0 + 14*x2 <= 187', 
        '13*x1 + 23*x3 <= 136', '6*x0 + 13*x1 <= 93', 
        '13*x1 + 14*x2 + 23*x3 <= 127', '6*x0 + 13*x1 + 14*x2 <= 121', 
        '6*x0 + 13*x1 + 23*x3 <= 58', '6*x0 + 13*x1 + 14*x2 + 23*x3 <= 58'
    ]
}
```