## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by George', 'hours worked by Paul', and 'hours worked by Peggy', which can be represented symbolically as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $5x_1 + 6x_2 + 5x_3$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
1. $2.1x_1 + 1.32x_3 \geq 21$
2. $5.73x_2 + 1.32x_3 \geq 18$
3. $2.1x_1 + 5.73x_2 + 1.32x_3 \geq 14$
4. $2.1x_1 + 5.73x_2 + 1.32x_3 \geq 14$ (Redundant with constraint 3)
5. $-10x_2 + 6x_3 \geq 0$
6. $9x_1 - 4x_2 \geq 0$
7. $2.1x_1 + 5.73x_2 \leq 59$
8. $5.73x_2 + 1.32x_3 \leq 31$
9. $x_1$ is an integer (Implicitly, $x_1 \geq 0$, $x_2 \geq 0$, $x_3 \geq 0$)

## 4: Remove redundant constraints and prepare for Gurobi implementation
Removing the redundant constraint:
The problem has been translated into:
- Minimize $5x_1 + 6x_2 + 5x_3$
- Subject to:
1. $2.1x_1 + 1.32x_3 \geq 21$
2. $5.73x_2 + 1.32x_3 \geq 18$
3. $2.1x_1 + 5.73x_2 + 1.32x_3 \geq 14$
4. $-10x_2 + 6x_3 \geq 0$
5. $9x_1 - 4x_2 \geq 0$
6. $2.1x_1 + 5.73x_2 \leq 59$
7. $5.73x_2 + 1.32x_3 \leq 31$
8. $x_1$ is an integer.

## 5: Implement the problem in Gurobi
```python
import gurobi

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

# Define the variables
x1 = m.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # hours worked by George
x2 = m.addVar(name="x2")  # hours worked by Paul
x3 = m.addVar(name="x3")  # hours worked by Peggy

# Objective function
m.setObjective(5 * x1 + 6 * x2 + 5 * x3, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(2.1 * x1 + 1.32 * x3 >= 21)
m.addConstr(5.73 * x2 + 1.32 * x3 >= 18)
m.addConstr(2.1 * x1 + 5.73 * x2 + 1.32 * x3 >= 14)
m.addConstr(-10 * x2 + 6 * x3 >= 0)
m.addConstr(9 * x1 - 4 * x2 >= 0)
m.addConstr(2.1 * x1 + 5.73 * x2 <= 59)
m.addConstr(5.73 * x2 + 1.32 * x3 <= 31)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by George: ", x1.varValue)
    print("Hours worked by Paul: ", x2.varValue)
    print("Hours worked by Peggy: ", x3.varValue)
else:
    print("The problem is infeasible")
```

## 6: Symbolic Representation
```json
{
    'sym_variables': [('x1', 'hours worked by George'), ('x2', 'hours worked by Paul'), ('x3', 'hours worked by Peggy')],
    'objective_function': '5*x1 + 6*x2 + 5*x3',
    'constraints': [
        '2.1*x1 + 1.32*x3 >= 21',
        '5.73*x2 + 1.32*x3 >= 18',
        '2.1*x1 + 5.73*x2 + 1.32*x3 >= 14',
        '-10*x2 + 6*x3 >= 0',
        '9*x1 - 4*x2 >= 0',
        '2.1*x1 + 5.73*x2 <= 59',
        '5.73*x2 + 1.32*x3 <= 31',
        'x1 is an integer'
    ]
}
```