## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by Bill' and 'hours worked by Bobby'. Let's denote 'hours worked by Bill' as $x_1$ and 'hours worked by Bobby' as $x_2$. The objective function to minimize is $4.11x_1 + 4.49x_2$.

## Step 2: List all constraints in symbolic notation
The constraints given are:
1. $4x_1 + 9x_2 \geq 38$
2. $x_1 + 3x_2 \geq 46$
3. $-2x_1 + 2x_2 \geq 0$
4. $4x_1 + 9x_2 \leq 87$
5. $x_1 + 3x_2 \leq 94$

## 3: Provide the symbolic representation of the problem
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'hours worked by Bill'), ('x2', 'hours worked by Bobby')],
'objective_function': '4.11*x1 + 4.49*x2',
'constraints': [
    '4*x1 + 9*x2 >= 38',
    'x1 + 3*x2 >= 46',
    '-2*x1 + 2*x2 >= 0',
    '4*x1 + 9*x2 <= 87',
    'x1 + 3*x2 <= 94'
]
}
```

## 4: Convert the problem into Gurobi code
Now, let's write the Gurobi code for this problem:
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="hours_worked_by_Bill", lb=0)  # Assuming hours cannot be negative
    x2 = model.addVar(name="hours_worked_by_Bobby", lb=0)  # Assuming hours cannot be negative

    # Define objective function
    model.setObjective(4.11 * x1 + 4.49 * x2, gurobi.GRB.MINIMIZE)

    # Define constraints
    model.addConstr(4 * x1 + 9 * x2 >= 38)
    model.addConstr(x1 + 3 * x2 >= 46)
    model.addConstr(-2 * x1 + 2 * x2 >= 0)
    model.addConstr(4 * x1 + 9 * x2 <= 87)
    model.addConstr(x1 + 3 * x2 <= 94)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Bill: {x1.varValue}")
        print(f"Hours worked by Bobby: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```