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

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $7.93x_0 + 3.2x_1 + 4.75x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $2x_0 = 2$ (work quality rating for George)
- $5x_0 = 5$ (paperwork competence rating for George)
- $9x_0 = 9$ (productivity rating for George)
- $9x_1 = 9$ (work quality rating for Peggy)
- $9x_1 = 9$ (paperwork competence rating for Peggy)
- $6x_1 = 6$ (productivity rating for Peggy)
- $7x_2 = 7$ (work quality rating for Hank)
- $6x_2 = 6$ (paperwork competence rating for Hank)
- $3x_2 = 3$ (productivity rating for Hank)
- $9x_1 + 7x_2 \geq 12$ (total combined work quality rating from Peggy and Hank)
- $2x_0 + 9x_1 + 7x_2 \geq 12$ (total combined work quality rating from George, Peggy, and Hank)
- $9x_1 + 6x_2 \geq 25$ (total combined paperwork competence rating from Peggy and Hank)
- $5x_0 + 9x_1 + 6x_2 \geq 16$ (total combined paperwork competence rating from George, Peggy, and Hank)
- $9x_0 + 6x_1 \geq 10$ (total combined productivity rating from George and Peggy)
- $9x_0 + 3x_2 \geq 14$ (total combined productivity rating from George and Hank)
- $9x_0 + 6x_1 + 3x_2 \geq 14$ (total combined productivity rating from George, Peggy, and Hank)
- $6x_0 - 4x_1 \geq 0$ (constraint involving George and Peggy's hours)
- $-10x_1 + 2x_2 \geq 0$ (constraint involving Peggy and Hank's hours)
- $5x_0 + 9x_1 \leq 38$ (total combined paperwork competence rating from George and Peggy)
- $9x_0 + 3x_2 \leq 31$ (total combined productivity rating from George and Hank)
- $6x_1 + 3x_2 \leq 53$ (total combined productivity rating from Peggy and Hank)
- $9x_0 + 6x_1 \leq 72$ (total combined productivity rating from George and Peggy)

## 4: Identify variable bounds
- $x_0$ can be non-integer
- $x_1$ must be an integer
- $x_2$ must be an integer

## 5: Formulate the problem in Gurobi
We will use Gurobi to solve this linear programming problem.

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x0 = m.addVar(name="hours_worked_by_George", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)
x1 = m.addVar(name="hours_worked_by_Peggy", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY, integrality=gp.GRB.INTEGER)
x2 = m.addVar(name="hours_worked_by_Hank", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY, integrality=gp.GRB.INTEGER)

# Objective function
m.setObjective(7.93*x0 + 3.2*x1 + 4.75*x2, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(2*x0 == 2, name="George_work_quality")
m.addConstr(5*x0 == 5, name="George_paperwork_competence")
m.addConstr(9*x0 == 9, name="George_productivity")

m.addConstr(9*x1 == 9, name="Peggy_work_quality")
m.addConstr(9*x1 == 9, name="Peggy_paperwork_competence")
m.addConstr(6*x1 == 6, name="Peggy_productivity")

m.addConstr(7*x2 == 7, name="Hank_work_quality")
m.addConstr(6*x2 == 6, name="Hank_paperwork_competence")
m.addConstr(3*x2 == 3, name="Hank_productivity")

m.addConstr(9*x1 + 7*x2 >= 12, name="combined_work_quality_Peggy_Hank")
m.addConstr(2*x0 + 9*x1 + 7*x2 >= 12, name="combined_work_quality_all")
m.addConstr(9*x1 + 6*x2 >= 25, name="combined_paperwork_competence_Peggy_Hank")
m.addConstr(5*x0 + 9*x1 + 6*x2 >= 16, name="combined_paperwork_competence_all")

m.addConstr(9*x0 + 6*x1 >= 10, name="combined_productivity_George_Peggy")
m.addConstr(9*x0 + 3*x2 >= 14, name="combined_productivity_George_Hank")
m.addConstr(9*x0 + 6*x1 + 3*x2 >= 14, name="combined_productivity_all")

m.addConstr(6*x0 - 4*x1 >= 0, name="George_Peggy_constraint")
m.addConstr(-10*x1 + 2*x2 >= 0, name="Peggy_Hank_constraint")

m.addConstr(5*x0 + 9*x1 <= 38, name="George_Peggy_paperwork_competence")
m.addConstr(9*x0 + 3*x2 <= 31, name="George_Hank_productivity")
m.addConstr(6*x1 + 3*x2 <= 53, name="Peggy_Hank_productivity")
m.addConstr(9*x0 + 6*x1 <= 72, name="George_Peggy_productivity")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by George: ", x0.varValue)
    print("Hours worked by Peggy: ", x1.varValue)
    print("Hours worked by Hank: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 6: Symbolic Representation
```json
{
    'sym_variables': [('x0', 'hours worked by George'), ('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Hank')],
    'objective_function': '7.93*x0 + 3.2*x1 + 4.75*x2',
    'constraints': [
        '2*x0 = 2',
        '5*x0 = 5',
        '9*x0 = 9',
        '9*x1 = 9',
        '9*x1 = 9',
        '6*x1 = 6',
        '7*x2 = 7',
        '6*x2 = 6',
        '3*x2 = 3',
        '9*x1 + 7*x2 >= 12',
        '2*x0 + 9*x1 + 7*x2 >= 12',
        '9*x1 + 6*x2 >= 25',
        '5*x0 + 9*x1 + 6*x2 >= 16',
        '9*x0 + 6*x1 >= 10',
        '9*x0 + 3*x2 >= 14',
        '9*x0 + 6*x1 + 3*x2 >= 14',
        '6*x0 - 4*x1 >= 0',
        '-10*x1 + 2*x2 >= 0',
        '5*x0 + 9*x1 <= 38',
        '9*x0 + 3*x2 <= 31',
        '6*x1 + 3*x2 <= 53',
        '9*x0 + 6*x1 <= 72'
    ]
}
```