## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Peggy', 'hours worked by Laura', 'hours worked by Bill', 'hours worked by Paul', 'hours worked by Mary'] which can be represented symbolically as 'x1', 'x2', 'x3', 'x4', 'x5' respectively.

## Step 2: Convert the problem description into a symbolic representation
The symbolic representation of the variables is:
- 'x1' for 'hours worked by Peggy'
- 'x2' for 'hours worked by Laura'
- 'x3' for 'hours worked by Bill'
- 'x4' for 'hours worked by Paul'
- 'x5' for 'hours worked by Mary'

## 3: Define the objective function in symbolic notation
The objective function to minimize is: $5.23x_1 + 3.46x_2 + 1.57x_3 + 4.21x_4 + 1.26x_5$

## 4: List the constraints in symbolic notation
The constraints are:
1. $16x_1 \geq 16$ (Peggy's computer competence rating is 16, but this seems to be an equality constraint, so $16x_1 = 16$ or simply $x_1 \geq 1$ if we consider the rating per hour)
2. $12x_2 \geq 12$ (Laura's computer competence rating is 12, similarly $x_2 \geq 1$)
3. $14x_3 \geq 14$ (Bill's computer competence rating is 14, so $x_3 \geq 1$)
4. $9x_4 \geq 9$ (Paul's computer competence rating is 9, so $x_4 \geq 1$)
5. $4x_5 \geq 4$ (Mary's computer competence rating is 4, so $x_5 \geq 1$)
6. $9x_4 + 4x_5 \geq 20$
7. $12x_2 + 14x_3 \geq 14$
8. $12x_2 + 4x_5 \geq 10$
9. $16x_1 + 12x_2 \geq 18$
10. $16x_1 + 4x_5 \geq 8$
11. $16x_1 + 9x_4 \geq 12$
12. $16x_1 + 14x_3 \geq 21$
13. $12x_2 + 9x_4 \geq 20$
14. $12x_2 + 9x_4 + 4x_5 \geq 15$
15. $12x_2 + 14x_3 + 9x_4 \geq 15$
16. $16x_1 + 12x_2 + 9x_4 \geq 15$
17. $12x_2 + 9x_4 + 4x_5 \geq 15$
18. $12x_2 + 14x_3 + 9x_4 \geq 15$
19. $16x_1 + 12x_2 + 9x_4 \geq 15$
20. $16x_1 + 12x_2 + 9x_4 \geq 15$
21. $16x_1 + 12x_2 + 9x_4 + 4x_5 \geq 15$
22. $-x_4 + 10x_5 \geq 0$
23. $-3x_1 + 10x_4 \geq 0$
24. $14x_3 + 9x_4 \leq 81$
25. $x_5$ is an integer.

## 5: Correcting and Simplifying Constraints
Correcting the interpretation of constraints 1 through 5:
- The actual constraints should directly relate to the computer competence ratings without assuming hourly rates, so:
1. $16x_1 \geq 16$
2. $12x_2 \geq 12$
3. $14x_3 \geq 14$
4. $9x_4 \geq 9$
5. $4x_5 \geq 4$

Simplifying:
1. $x_1 \geq 1$
2. $x_2 \geq 1$
3. $x_3 \geq 1$
4. $x_4 \geq 1$
5. $x_5 \geq 1$

## 6: Formulate the problem in Gurobi
```python
import gurobi as gp

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

# Define the variables
x1 = m.addVar(name="hours_worked_by_Peggy", lb=0)  # Can be fractional
x2 = m.addVar(name="hours_worked_by_Laura", lb=0)  # Can be fractional
x3 = m.addVar(name="hours_worked_by_Bill", lb=0)  # Can be fractional
x4 = m.addVar(name="hours_worked_by_Paul", lb=0)  # Can be fractional
x5 = m.addVar(name="hours_worked_by_Mary", lb=0, type=gp.GRB.INTEGER)  # Must be integer

# Objective function
m.setObjective(5.23*x1 + 3.46*x2 + 1.57*x3 + 4.21*x4 + 1.26*x5, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(x1 >= 1)
m.addConstr(x2 >= 1)
m.addConstr(x3 >= 1)
m.addConstr(x4 >= 1)
m.addConstr(x5 >= 1)

m.addConstr(9*x4 + 4*x5 >= 20)
m.addConstr(12*x2 + 14*x3 >= 14)
m.addConstr(12*x2 + 4*x5 >= 10)
m.addConstr(16*x1 + 12*x2 >= 18)
m.addConstr(16*x1 + 4*x5 >= 8)
m.addConstr(16*x1 + 9*x4 >= 12)
m.addConstr(16*x1 + 14*x3 >= 21)
m.addConstr(12*x2 + 9*x4 >= 20)
m.addConstr(12*x2 + 9*x4 + 4*x5 >= 15)
m.addConstr(12*x2 + 14*x3 + 9*x4 >= 15)
m.addConstr(16*x1 + 12*x2 + 9*x4 >= 15)
m.addConstr(12*x2 + 9*x4 + 4*x5 >= 15)
m.addConstr(12*x2 + 14*x3 + 9*x4 >= 15)
m.addConstr(16*x1 + 12*x2 + 9*x4 >= 15)
m.addConstr(16*x1 + 12*x2 + 9*x4 + 4*x5 >= 15)
m.addConstr(-x4 + 10*x5 >= 0)
m.addConstr(-3*x1 + 10*x4 >= 0)
m.addConstr(14*x3 + 9*x4 <= 81)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by Peggy: ", x1.varValue)
    print("Hours worked by Laura: ", x2.varValue)
    print("Hours worked by Bill: ", x3.varValue)
    print("Hours worked by Paul: ", x4.varValue)
    print("Hours worked by Mary: ", x5.varValue)
else:
    print("The problem is infeasible")
```

## 7: Symbolic Representation
```json
{
    'sym_variables': [('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Laura'), ('x3', 'hours worked by Bill'), ('x4', 'hours worked by Paul'), ('x5', 'hours worked by Mary')],
    'objective_function': '5.23*x1 + 3.46*x2 + 1.57*x3 + 4.21*x4 + 1.26*x5',
    'constraints': [
        'x1 >= 1',
        'x2 >= 1',
        'x3 >= 1',
        'x4 >= 1',
        'x5 >= 1',
        '9*x4 + 4*x5 >= 20',
        '12*x2 + 14*x3 >= 14',
        '12*x2 + 4*x5 >= 10',
        '16*x1 + 12*x2 >= 18',
        '16*x1 + 4*x5 >= 8',
        '16*x1 + 9*x4 >= 12',
        '16*x1 + 14*x3 >= 21',
        '12*x2 + 9*x4 >= 20',
        '12*x2 + 9*x4 + 4*x5 >= 15',
        '12*x2 + 14*x3 + 9*x4 >= 15',
        '16*x1 + 12*x2 + 9*x4 >= 15',
        '12*x2 + 9*x4 + 4*x5 >= 15',
        '12*x2 + 14*x3 + 9*x4 >= 15',
        '16*x1 + 12*x2 + 9*x4 >= 15',
        '16*x1 + 12*x2 + 9*x4 + 4*x5 >= 15',
        '-x4 + 10*x5 >= 0',
        '-3*x1 + 10*x4 >= 0',
        '14*x3 + 9*x4 <= 81'
    ]
}
```