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

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $2x_0 + 4x_1 + 5x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $12x_0 \leq 73$
- $4x_0 \leq 105$
- $15x_0 \leq 117$
- $12x_0 \leq 81$
- $17x_1 \leq 73$
- $15x_1 \leq 105$
- $2x_1 \leq 117$
- $2x_1 \leq 81$
- $2x_2 \leq 73$
- $12x_2 \leq 105$
- $13x_2 \leq 117$
- $4x_2 \leq 81$
- $17x_1 + 2x_2 \geq 17$
- $12x_0 + 2x_2 \geq 15$
- $12x_0 + 17x_1 + 2x_2 \geq 15$
- $15x_1 + 12x_2 \geq 27$
- $4x_0 + 15x_1 + 12x_2 \geq 27$
- $15x_0 + 13x_2 \geq 28$
- $2x_1 + 13x_2 \geq 26$
- $15x_0 + 2x_1 \geq 31$
- $15x_0 + 2x_1 + 13x_2 \geq 31$
- $12x_0 + 2x_1 \geq 11$
- $12x_0 + 4x_2 \geq 17$
- $12x_0 + 2x_1 + 4x_2 \geq 17$
- $-4x_1 + 6x_2 \geq 0$
- $6x_0 - 2x_1 \geq 0$
- $6x_0 - 3x_2 \geq 0$
- $15x_0 + 2x_1 \leq 108$
- $2x_1 + 13x_2 \leq 89$
- $15x_0 + 2x_1 + 13x_2 \leq 43$

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

## 5: Implement the objective function and constraints in Gurobi
We will use Gurobi's Python API to implement the model.

```python
import gurobi as gp

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

# Define the variables
x0 = m.addVar(name="hours_worked_by_Dale", lb=0)
x1 = m.addVar(name="hours_worked_by_Bobby", lb=0)
x2 = m.addVar(name="hours_worked_by_Jean", lb=0)

# Objective function
m.setObjective(2*x0 + 4*x1 + 5*x2, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(12*x0 <= 73)
m.addConstr(4*x0 <= 105)
m.addConstr(15*x0 <= 117)
m.addConstr(12*x0 <= 81)
m.addConstr(17*x1 <= 73)
m.addConstr(15*x1 <= 105)
m.addConstr(2*x1 <= 117)
m.addConstr(2*x1 <= 81)
m.addConstr(2*x2 <= 73)
m.addConstr(12*x2 <= 105)
m.addConstr(13*x2 <= 117)
m.addConstr(4*x2 <= 81)
m.addConstr(17*x1 + 2*x2 >= 17)
m.addConstr(12*x0 + 2*x2 >= 15)
m.addConstr(12*x0 + 17*x1 + 2*x2 >= 15)
m.addConstr(15*x1 + 12*x2 >= 27)
m.addConstr(4*x0 + 15*x1 + 12*x2 >= 27)
m.addConstr(15*x0 + 13*x2 >= 28)
m.addConstr(2*x1 + 13*x2 >= 26)
m.addConstr(15*x0 + 2*x1 >= 31)
m.addConstr(15*x0 + 2*x1 + 13*x2 >= 31)
m.addConstr(12*x0 + 2*x1 >= 11)
m.addConstr(12*x0 + 4*x2 >= 17)
m.addConstr(12*x0 + 2*x1 + 4*x2 >= 17)
m.addConstr(-4*x1 + 6*x2 >= 0)
m.addConstr(6*x0 - 2*x1 >= 0)
m.addConstr(6*x0 - 3*x2 >= 0)
m.addConstr(15*x0 + 2*x1 <= 108)
m.addConstr(2*x1 + 13*x2 <= 89)
m.addConstr(15*x0 + 2*x1 + 13*x2 <= 43)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Hours worked by Dale:", x0.varValue)
    print("Hours worked by Bobby:", x1.varValue)
    print("Hours worked by Jean:", x2.varValue)
    print("Objective function value:", m.objVal)
else:
    print("No optimal solution found.")
```

```json
{
    'sym_variables': [
        ('x0', 'hours worked by Dale'), 
        ('x1', 'hours worked by Bobby'), 
        ('x2', 'hours worked by Jean')
    ], 
    'objective_function': '2*x0 + 4*x1 + 5*x2', 
    'constraints': [
        '12*x0 <= 73', 
        '4*x0 <= 105', 
        '15*x0 <= 117', 
        '12*x0 <= 81', 
        '17*x1 <= 73', 
        '15*x1 <= 105', 
        '2*x1 <= 117', 
        '2*x1 <= 81', 
        '2*x2 <= 73', 
        '12*x2 <= 105', 
        '13*x2 <= 117', 
        '4*x2 <= 81', 
        '17*x1 + 2*x2 >= 17', 
        '12*x0 + 2*x2 >= 15', 
        '12*x0 + 17*x1 + 2*x2 >= 15', 
        '15*x1 + 12*x2 >= 27', 
        '4*x0 + 15*x1 + 12*x2 >= 27', 
        '15*x0 + 13*x2 >= 28', 
        '2*x1 + 13*x2 >= 26', 
        '15*x0 + 2*x1 >= 31', 
        '15*x0 + 2*x1 + 13*x2 >= 31', 
        '12*x0 + 2*x1 >= 11', 
        '12*x0 + 4*x2 >= 17', 
        '12*x0 + 2*x1 + 4*x2 >= 17', 
        '-4*x1 + 6*x2 >= 0', 
        '6*x0 - 2*x1 >= 0', 
        '6*x0 - 3*x2 >= 0', 
        '15*x0 + 2*x1 <= 108', 
        '2*x1 + 13*x2 <= 89', 
        '15*x0 + 2*x1 + 13*x2 <= 43'
    ]
}
```