## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to various constraints. The variables are:
- $x_0$: hours worked by George
- $x_1$: hours worked by John
- $x_2$: hours worked by Laura
- $x_3$: hours worked by Bobby
- $x_4$: hours worked by Mary
- $x_5$: hours worked by Hank
- $x_6$: hours worked by Paul

## Step 2: Express the objective function in symbolic notation
The objective function to maximize is:
\[ 6.15x_0 + 4.52x_1 + 6.66x_2 + 7.61x_3 + 1.6x_4 + 4.75x_5 + 6.55x_6 \]

## Step 3: List the constraints in symbolic notation
Constraints include:
- Computer competence ratings
- Likelihood to quit indices
- Work quality ratings
- Organization scores
- Paperwork competence ratings
And others as detailed in the problem description.

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

# Define the model
model = gp.Model("optimization_problem")

# Define the variables
x = model.addVars(7, name="hours_worked", lb=0)

# Set the variable names for easier reference
x[0].setAttr("Name", "George")
x[1].setAttr("Name", "John")
x[2].setAttr("Name", "Laura")
x[3].setAttr("Name", "Bobby")
x[4].setAttr("Name", "Mary")
x[5].setAttr("Name", "Hank")
x[6].setAttr("Name", "Paul")

# Define the objective function
model.setObjective(6.15*x[0] + 4.52*x[1] + 6.66*x[2] + 7.61*x[3] + 1.6*x[4] + 4.75*x[5] + 6.55*x[6], gp.GRB.MAXIMIZE)

# Add constraints
# George's ratings
model.addConstr(9*x[0] <= 747)  # Computer
model.addConstr(33*x[0] <= 734)  # Likelihood to quit
model.addConstr(14*x[0] <= 804)  # Work quality
model.addConstr(24*x[0] <= 752)  # Organization
model.addConstr(8*x[0] <= 685)  # Paperwork

# John's ratings
model.addConstr(8*x[1] <= 747)  # Computer
model.addConstr(20*x[1] <= 734)  # Likelihood to quit
model.addConstr(17*x[1] <= 804)  # Work quality
model.addConstr(10*x[1] <= 752)  # Organization
model.addConstr(13*x[1] <= 685)  # Paperwork

# Laura's ratings
model.addConstr(24*x[2] <= 747)  # Computer
model.addConstr(4*x[2] <= 734)  # Likelihood to quit
model.addConstr(8*x[2] <= 804)  # Work quality
model.addConstr(26*x[2] <= 752)  # Organization
model.addConstr(17*x[2] <= 685)  # Paperwork

# Bobby's ratings
model.addConstr(34*x[3] <= 747)  # Computer
model.addConstr(13*x[3] <= 734)  # Likelihood to quit
model.addConstr(9*x[3] <= 804)  # Work quality
model.addConstr(15*x[3] <= 752)  # Organization
model.addConstr(18*x[3] <= 685)  # Paperwork

# Mary's ratings
model.addConstr(34*x[4] <= 747)  # Computer
model.addConstr(x[4] <= 734)  # Likelihood to quit
model.addConstr(21*x[4] <= 804)  # Work quality
model.addConstr(3*x[4] <= 752)  # Organization
model.addConstr(35*x[4] <= 685)  # Paperwork

# Hank's ratings
model.addConstr(3*x[5] <= 747)  # Computer
model.addConstr(11*x[5] <= 734)  # Likelihood to quit
model.addConstr(25*x[5] <= 804)  # Work quality
model.addConstr(23*x[5] <= 752)  # Organization
model.addConstr(4*x[5] <= 685)  # Paperwork

# Paul's ratings
model.addConstr(20*x[6] <= 747)  # Computer
model.addConstr(5*x[6] <= 734)  # Likelihood to quit
model.addConstr(15*x[6] <= 804)  # Work quality
model.addConstr(2*x[6] <= 752)  # Organization
model.addConstr(24*x[6] <= 685)  # Paperwork

# Other constraints
model.addConstr(24*x[2] + 34*x[3] >= 95)  # Computer Laura, Bobby
model.addConstr(9*x[0] + 8*x[1] >= 41)  # Computer George, John
model.addConstr(8*x[1] + 13*x[4] >= 104)  # Computer John, Mary
model.addConstr(24*x[2] + 20*x[6] >= 88)  # Computer Laura, Paul
model.addConstr(34*x[3] + 17*x[1] >= 42)  # Computer Bobby, John
model.addConstr(24*x[2] + 8*x[1] >= 50)  # Computer Laura, John
model.addConstr(9*x[0] + 8*x[1] >= 37)  # Computer George, John

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    for i in range(7):
        print(f"Hours worked by {['George', 'John', 'Laura', 'Bobby', 'Mary', 'Hank', 'Paul'][i]}: {x[i].varValue}")
else:
    print("No optimal solution found")
```

## Step 5: Symbolic Representation
```json
{
    'sym_variables': [('x0', 'hours worked by George'), ('x1', 'hours worked by John'), ('x2', 'hours worked by Laura'), ('x3', 'hours worked by Bobby'), ('x4', 'hours worked by Mary'), ('x5', 'hours worked by Hank'), ('x6', 'hours worked by Paul')],
    'objective_function': '6.15*x0 + 4.52*x1 + 6.66*x2 + 7.61*x3 + 1.6*x4 + 4.75*x5 + 6.55*x6',
    'constraints': [
        '9*x0 <= 747', '33*x0 <= 734', '14*x0 <= 804', '24*x0 <= 752', '8*x0 <= 685',
        '8*x1 <= 747', '20*x1 <= 734', '17*x1 <= 804', '10*x1 <= 752', '13*x1 <= 685',
        '24*x2 <= 747', '4*x2 <= 734', '8*x2 <= 804', '26*x2 <= 752', '17*x2 <= 685',
        '34*x3 <= 747', '13*x3 <= 734', '9*x3 <= 804', '15*x3 <= 752', '18*x3 <= 685',
        '34*x4 <= 747', '*x4 <= 734', '21*x4 <= 804', '3*x4 <= 752', '35*x4 <= 685',
        '3*x5 <= 747', '11*x5 <= 734', '25*x5 <= 804', '23*x5 <= 752', '4*x5 <= 685',
        '20*x6 <= 747', '5*x6 <= 734', '15*x6 <= 804', '2*x6 <= 752', '24*x6 <= 685',
        '24*x2 + 34*x3 >= 95', '9*x0 + 8*x1 >= 41', '8*x1 + 13*x4 >= 104', 
        '24*x2 + 20*x6 >= 88', '34*x3 + 17*x1 >= 42', '24*x2 + 8*x1 >= 50', 
        '9*x0 + 8*x1 >= 37'
    ]
}
```