## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Bobby', 'hours worked by Laura', 'hours worked by Paul', 'hours worked by Dale', '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 $7x_0 + 9x_1 + 5x_2 + 8x_3 + 9x_4$.

## Step 3: List the constraints
1. $4x_1 + 7x_2 \geq 101$
2. $7x_2 + 21x_3 \geq 86$
3. $26x_0 + 4x_1 + 7x_2 + 21x_3 + 14x_4 \geq 86$
4. $11x_0 + 25x_2 \geq 39$
5. $21x_1 + 25x_2 \geq 46$
6. $21x_1 + 16x_4 \geq 54$
7. $11x_0 + 22x_3 \geq 28$
8. $11x_0 + 4x_1 + 22x_3 \geq 54$
9. $21x_1 + 22x_3 + 16x_4 \geq 54$
10. $11x_0 + 22x_3 + 16x_4 \geq 54$
11. $25x_2 + 22x_3 + 16x_4 \geq 54$
12. $11x_0 + 4x_1 + 22x_3 \geq 55$
13. $21x_1 + 22x_3 + 16x_4 \geq 55$
14. $11x_0 + 22x_3 + 16x_4 \geq 55$
15. $25x_2 + 22x_3 + 16x_4 \geq 55$
16. $11x_0 + 4x_1 + 22x_3 \geq 69$
17. $21x_1 + 22x_3 + 16x_4 \geq 69$
18. $11x_0 + 22x_3 + 16x_4 \geq 69$
19. $25x_2 + 22x_3 + 16x_4 \geq 69$
20. $11x_0 + 21x_1 + 22x_3 \geq 43$
21. $21x_1 + 22x_3 + 16x_4 \geq 43$
22. $11x_0 + 22x_3 + 16x_4 \geq 43$
23. $25x_2 + 22x_3 + 16x_4 \geq 43$
24. $11x_0 + 21x_1 + 25x_2 + 22x_3 + 16x_4 \geq 43$
25. $4x_1 + 14x_4 \leq 541$
26. $26x_0 + 14x_4 \leq 592$
27. $4x_1 + 7x_2 \leq 626$
28. $26x_0 + 7x_2 \leq 436$
29. $21x_3 + 14x_4 \leq 769$
30. $4x_1 + 7x_2 + 21x_3 \leq 676$
31. $26x_0 + 7x_2 + 21x_3 \leq 845$
32. $26x_0 + 4x_1 + 7x_2 \leq 625$
33. $4x_1 + 7x_2 + 16x_4 \leq 575$
34. $26x_0 + 4x_1 + 21x_3 \leq 400$
35. $25x_2 + 22x_3 \leq 333$
36. $11x_0 + 22x_3 \leq 286$
37. $21x_1 + 16x_4 \leq 226$
38. $21x_1 + 22x_3 \leq 342$
39. $22x_3 + 16x_4 \leq 110$
40. $25x_2 + 16x_4 \leq 111$

## 4: Define the variable bounds and types
- $x_0$ is continuous
- $x_1$ is continuous
- $x_2$ is integer
- $x_3$ is continuous
- $x_4$ is integer

## 5: Write the Gurobi code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x0", vtype=gurobi.GRB.CONTINUOUS)
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x1", vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x2", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x3", vtype=gurobi.GRB.CONTINUOUS)
    x4 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x4", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(7 * x0 + 9 * x1 + 5 * x2 + 8 * x3 + 9 * x4, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(4 * x1 + 7 * x2 >= 101)
    model.addConstr(7 * x2 + 21 * x3 >= 86)
    model.addConstr(26 * x0 + 4 * x1 + 7 * x2 + 21 * x3 + 14 * x4 >= 86)
    model.addConstr(11 * x0 + 25 * x2 >= 39)
    model.addConstr(21 * x1 + 25 * x2 >= 46)
    model.addConstr(21 * x1 + 16 * x4 >= 54)
    model.addConstr(11 * x0 + 22 * x3 >= 28)
    model.addConstr(11 * x0 + 4 * x1 + 22 * x3 >= 54)
    model.addConstr(21 * x1 + 22 * x3 + 16 * x4 >= 54)
    model.addConstr(11 * x0 + 22 * x3 + 16 * x4 >= 54)
    model.addConstr(25 * x2 + 22 * x3 + 16 * x4 >= 54)
    model.addConstr(11 * x0 + 4 * x1 + 22 * x3 >= 55)
    model.addConstr(21 * x1 + 22 * x3 + 16 * x4 >= 55)
    model.addConstr(11 * x0 + 22 * x3 + 16 * x4 >= 55)
    model.addConstr(25 * x2 + 22 * x3 + 16 * x4 >= 55)
    model.addConstr(11 * x0 + 4 * x1 + 22 * x3 >= 69)
    model.addConstr(21 * x1 + 22 * x3 + 16 * x4 >= 69)
    model.addConstr(11 * x0 + 22 * x3 + 16 * x4 >= 69)
    model.addConstr(25 * x2 + 22 * x3 + 16 * x4 >= 69)
    model.addConstr(11 * x0 + 21 * x1 + 22 * x3 >= 43)
    model.addConstr(21 * x1 + 22 * x3 + 16 * x4 >= 43)
    model.addConstr(11 * x0 + 22 * x3 + 16 * x4 >= 43)
    model.addConstr(25 * x2 + 22 * x3 + 16 * x4 >= 43)
    model.addConstr(11 * x0 + 21 * x1 + 25 * x2 + 22 * x3 + 16 * x4 >= 43)
    model.addConstr(4 * x1 + 14 * x4 <= 541)
    model.addConstr(26 * x0 + 14 * x4 <= 592)
    model.addConstr(4 * x1 + 7 * x2 <= 626)
    model.addConstr(26 * x0 + 7 * x2 <= 436)
    model.addConstr(21 * x3 + 14 * x4 <= 769)
    model.addConstr(4 * x1 + 7 * x2 + 21 * x3 <= 676)
    model.addConstr(26 * x0 + 7 * x2 + 21 * x3 <= 845)
    model.addConstr(26 * x0 + 4 * x1 + 7 * x2 <= 625)
    model.addConstr(4 * x1 + 7 * x2 + 16 * x4 <= 575)
    model.addConstr(26 * x0 + 4 * x1 + 21 * x3 <= 400)
    model.addConstr(25 * x2 + 22 * x3 <= 333)
    model.addConstr(11 * x0 + 22 * x3 <= 286)
    model.addConstr(21 * x1 + 16 * x4 <= 226)
    model.addConstr(21 * x1 + 22 * x3 <= 342)
    model.addConstr(22 * x3 + 16 * x4 <= 110)
    model.addConstr(25 * x2 + 16 * x4 <= 111)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
        print("x3: ", x3.varValue)
        print("x4: ", x4.varValue)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```

## 6: Symbolic representation
```json
{
    'sym_variables': [('x0', 'hours worked by Bobby'), ('x1', 'hours worked by Laura'), ('x2', 'hours worked by Paul'), ('x3', 'hours worked by Dale'), ('x4', 'hours worked by John')],
    'objective_function': '7*x0 + 9*x1 + 5*x2 + 8*x3 + 9*x4',
    'constraints': [
        '4*x1 + 7*x2 >= 101',
        '7*x2 + 21*x3 >= 86',
        '26*x0 + 4*x1 + 7*x2 + 21*x3 + 14*x4 >= 86',
        '11*x0 + 25*x2 >= 39',
        '21*x1 + 25*x2 >= 46',
        '21*x1 + 16*x4 >= 54',
        '11*x0 + 22*x3 >= 28',
        '11*x0 + 4*x1 + 22*x3 >= 54',
        '21*x1 + 22*x3 + 16*x4 >= 54',
        '11*x0 + 22*x3 + 16*x4 >= 54',
        '25*x2 + 22*x3 + 16*x4 >= 54',
        '11*x0 + 4*x1 + 22*x3 >= 55',
        '21*x1 + 22*x3 + 16*x4 >= 55',
        '11*x0 + 22*x3 + 16*x4 >= 55',
        '25*x2 + 22*x3 + 16*x4 >= 55',
        '11*x0 + 4*x1 + 22*x3 >= 69',
        '21*x1 + 22*x3 + 16*x4 >= 69',
        '11*x0 + 22*x3 + 16*x4 >= 69',
        '25*x2 + 22*x3 + 16*x4 >= 69',
        '11*x0 + 21*x1 + 22*x3 >= 43',
        '21*x1 + 22*x3 + 16*x4 >= 43',
        '11*x0 + 22*x3 + 16*x4 >= 43',
        '25*x2 + 22*x3 + 16*x4 >= 43',
        '11*x0 + 21*x1 + 25*x2 + 22*x3 + 16*x4 >= 43',
        '4*x1 + 14*x4 <= 541',
        '26*x0 + 14*x4 <= 592',
        '4*x1 + 7*x2 <= 626',
        '26*x0 + 7*x2 <= 436',
        '21*x3 + 14*x4 <= 769',
        '4*x1 + 7*x2 + 21*x3 <= 676',
        '26*x0 + 7*x2 + 21*x3 <= 845',
        '26*x0 + 4*x1 + 7*x2 <= 625',
        '4*x1 + 7*x2 + 16*x4 <= 575',
        '26*x0 + 4*x1 + 21*x3 <= 400',
        '25*x2 + 22*x3 <= 333',
        '11*x0 + 22*x3 <= 286',
        '21*x1 + 16*x4 <= 226',
        '21*x1 + 22*x3 <= 342',
        '22*x3 + 16*x4 <= 110',
        '25*x2 + 16*x4 <= 111'
    ]
}
```