## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Jean', 'hours worked by Hank', 'hours worked by Bobby', and 'hours worked by Ringo', which can be represented symbolically as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $2x_0 + 2x_1 + 9x_2 + 7x_3$.

## Step 3: List the constraints in symbolic notation
1. Productivity rating constraints:
- $23x_0 \leq 878$
- $32x_1 \leq 878$
- $17x_2 \leq 878$
- $12x_3 \leq 878$
- Computer competence rating constraints:
- $27x_0 \leq 333$
- $15x_1 \leq 333$
- $10x_2 \leq 333$
- $10x_3 \leq 333$

## 4: Additional constraints
- $32x_1 + 17x_2 \geq 205$
- $23x_0 + 32x_1 + 17x_2 + 12x_3 \geq 205$
- $10x_2 + 10x_3 \geq 64$
- $15x_1 + 10x_3 \geq 70$
- $27x_0 + 10x_3 \geq 67$
- $27x_0 + 15x_1 + 10x_2 + 10x_3 \geq 67$
- $-7x_0 + 4x_2 \geq 0$
- $8x_2 - 6x_3 \geq 0$
- $-10x_1 + 2x_2 + 4x_3 \geq 0$
- $23x_0 + 32x_1 + 12x_3 \leq 632$
- $15x_1 + 10x_3 \leq 331$
- $10x_2 + 10x_3 \leq 170$
- $27x_0 + 10x_3 \leq 228$
- $27x_0 + 15x_1 \leq 130$
- $27x_0 + 10x_2 \leq 118$
- $27x_0 + 15x_1 + 10x_2 \leq 295$

## 5: Symbolic Representation
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Jean'), 
        ('x1', 'hours worked by Hank'), 
        ('x2', 'hours worked by Bobby'), 
        ('x3', 'hours worked by Ringo')
    ], 
    'objective_function': '2*x0 + 2*x1 + 9*x2 + 7*x3', 
    'constraints': [
        '23*x0 <= 878', '32*x1 <= 878', '17*x2 <= 878', '12*x3 <= 878',
        '27*x0 <= 333', '15*x1 <= 333', '10*x2 <= 333', '10*x3 <= 333',
        '32*x1 + 17*x2 >= 205', '23*x0 + 32*x1 + 17*x2 + 12*x3 >= 205',
        '10*x2 + 10*x3 >= 64', '15*x1 + 10*x3 >= 70', '27*x0 + 10*x3 >= 67',
        '27*x0 + 15*x1 + 10*x2 + 10*x3 >= 67', '-7*x0 + 4*x2 >= 0',
        '8*x2 - 6*x3 >= 0', '-10*x1 + 2*x2 + 4*x3 >= 0',
        '23*x0 + 32*x1 + 12*x3 <= 632', '15*x1 + 10*x3 <= 331',
        '10*x2 + 10*x3 <= 170', '27*x0 + 10*x3 <= 228',
        '27*x0 + 15*x1 <= 130', '27*x0 + 10*x2 <= 118',
        '27*x0 + 15*x1 + 10*x2 <= 295'
    ]
}
```

## 6: Gurobi Code
```python
import gurobi

def optimization_problem():
    model = gurobi.Model()

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

    # Objective function
    model.setObjective(2*x0 + 2*x1 + 9*x2 + 7*x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(23*x0 <= 878)
    model.addConstr(32*x1 <= 878)
    model.addConstr(17*x2 <= 878)
    model.addConstr(12*x3 <= 878)

    model.addConstr(27*x0 <= 333)
    model.addConstr(15*x1 <= 333)
    model.addConstr(10*x2 <= 333)
    model.addConstr(10*x3 <= 333)

    model.addConstr(32*x1 + 17*x2 >= 205)
    model.addConstr(23*x0 + 32*x1 + 17*x2 + 12*x3 >= 205)
    model.addConstr(10*x2 + 10*x3 >= 64)
    model.addConstr(15*x1 + 10*x3 >= 70)
    model.addConstr(27*x0 + 10*x3 >= 67)
    model.addConstr(27*x0 + 15*x1 + 10*x2 + 10*x3 >= 67)

    model.addConstr(-7*x0 + 4*x2 >= 0)
    model.addConstr(8*x2 - 6*x3 >= 0)
    model.addConstr(-10*x1 + 2*x2 + 4*x3 >= 0)

    model.addConstr(23*x0 + 32*x1 + 12*x3 <= 632)
    model.addConstr(15*x1 + 10*x3 <= 331)
    model.addConstr(10*x2 + 10*x3 <= 170)
    model.addConstr(27*x0 + 10*x3 <= 228)
    model.addConstr(27*x0 + 15*x1 <= 130)
    model.addConstr(27*x0 + 10*x2 <= 118)
    model.addConstr(27*x0 + 15*x1 + 10*x2 <= 295)

    # Solve the model
    model.optimize()

    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Jean: {x0.varValue}")
        print(f"Hours worked by Hank: {x1.varValue}")
        print(f"Hours worked by Bobby: {x2.varValue}")
        print(f"Hours worked by Ringo: {x3.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimization_problem()
```