## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Bobby', 'hours worked by Dale', 'hours worked by Peggy', 'hours worked by Paul', 'hours worked by John']. Let's denote them as $x_0, x_1, x_2, x_3, x_4$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to minimize is $7.36x_0 + 9.14x_1 + 6.94x_2 + 1.22x_3 + 5.42x_4$.

## Step 3: List the constraints
1. $4x_0 \leq 83$ is not needed as it's a variable attribute
2. $2x_0 \leq 85$ is not needed as it's a variable attribute
3. $2x_1 \leq 83$ is not needed as it's a variable attribute
4. $1x_1 \leq 85$ is not needed as it's a variable attribute
5. $2x_2 \leq 83$ is not needed as it's a variable attribute
6. $2x_2 \leq 85$ is not needed as it's a variable attribute
7. $7x_3 \leq 83$ is not needed as it's a variable attribute
8. $1x_3 \leq 85$ is not needed as it's a variable attribute
9. $1x_4 \leq 83$ is not needed as it's a variable attribute
10. $5x_4 \leq 85$ is not needed as it's a variable attribute
11. $4x_0 + 2x_2 \geq 13$
12. $2x_1 + 2x_2 \geq 11$
13. $2x_2 + 1x_4 \geq 5$
14. $7x_3 + 1x_4 \geq 5$
15. $4x_0 + 2x_1 + 2x_2 + 7x_3 + 1x_4 \geq 5$
16. $2x_0 + 1x_3 \geq 10$
17. $2x_0 + 1x_1 \geq 5$
18. $2x_0 + 2x_2 \geq 13$
19. $2x_0 + 1x_1 + 2x_2 + 1x_3 + 5x_4 \geq 13$
20. $-5x_2 + 4x_4 \geq 0$
21. $2x_1 + 2x_2 \leq 33$
22. $4x_0 + 2x_2 \leq 81$
23. $2x_1 + 1x_4 \leq 24$
24. $2x_1 + 2x_2 + 7x_3 \leq 50$
25. $2x_1 + 7x_3 + 1x_4 \leq 25$
26. $1x_1 + 1x_3 \leq 50$
27. $1x_1 + 5x_4 \leq 72$

## Step 4: Create the Gurobi model and variables
We will now create the Gurobi model and variables.

## 5: Implement the objective function and constraints in Gurobi

Here is the solution:

```json
{
    'sym_variables': [
        ('x0', 'hours worked by Bobby'), 
        ('x1', 'hours worked by Dale'), 
        ('x2', 'hours worked by Peggy'), 
        ('x3', 'hours worked by Paul'), 
        ('x4', 'hours worked by John')
    ], 
    'objective_function': '7.36*x0 + 9.14*x1 + 6.94*x2 + 1.22*x3 + 5.42*x4', 
    'constraints': [
        '4*x0 + 2*x2 >= 13',
        '2*x1 + 2*x2 >= 11',
        '2*x2 + x4 >= 5',
        '7*x3 + x4 >= 5',
        '4*x0 + 2*x1 + 2*x2 + 7*x3 + x4 >= 5',
        '2*x0 + x3 >= 10',
        '2*x0 + x1 >= 5',
        '2*x0 + 2*x2 >= 13',
        '2*x0 + x1 + 2*x2 + x3 + 5*x4 >= 13',
        '-5*x2 + 4*x4 >= 0',
        '2*x1 + 2*x2 <= 33',
        '4*x0 + 2*x2 <= 81',
        '2*x1 + x4 <= 24',
        '2*x1 + 2*x2 + 7*x3 <= 50',
        '2*x1 + 7*x3 + x4 <= 25',
        'x1 + x3 <= 50',
        'x1 + 5*x4 <= 72'
    ]
}
```

```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Bobby
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Dale
    x2 = model.addVar(name="x2", lb=0)  # hours worked by Peggy
    x3 = model.addVar(name="x3", lb=0)  # hours worked by Paul
    x4 = model.addVar(name="x4", lb=0)  # hours worked by John

    # Objective function
    model.setObjective(7.36 * x0 + 9.14 * x1 + 6.94 * x2 + 1.22 * x3 + 5.42 * x4, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(4 * x0 + 2 * x2 >= 13)
    model.addConstr(2 * x1 + 2 * x2 >= 11)
    model.addConstr(2 * x2 + x4 >= 5)
    model.addConstr(7 * x3 + x4 >= 5)
    model.addConstr(4 * x0 + 2 * x1 + 2 * x2 + 7 * x3 + x4 >= 5)
    model.addConstr(2 * x0 + x3 >= 10)
    model.addConstr(2 * x0 + x1 >= 5)
    model.addConstr(2 * x0 + 2 * x2 >= 13)
    model.addConstr(2 * x0 + x1 + 2 * x2 + x3 + 5 * x4 >= 13)
    model.addConstr(-5 * x2 + 4 * x4 >= 0)
    model.addConstr(2 * x1 + 2 * x2 <= 33)
    model.addConstr(4 * x0 + 2 * x2 <= 81)
    model.addConstr(2 * x1 + x4 <= 24)
    model.addConstr(2 * x1 + 2 * x2 + 7 * x3 <= 50)
    model.addConstr(2 * x1 + 7 * x3 + x4 <= 25)
    model.addConstr(x1 + x3 <= 50)
    model.addConstr(x1 + 5 * x4 <= 72)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Hours worked by Bobby: ", x0.varValue)
        print("Hours worked by Dale: ", x1.varValue)
        print("Hours worked by Peggy: ", x2.varValue)
        print("Hours worked by Paul: ", x3.varValue)
        print("Hours worked by John: ", x4.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```