## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of face masks
- $x_2$ represents the number of hand sanitizers

## Step 2: Translate the objective function into symbolic notation
The profit from selling face masks is $1 \cdot x_1$ and from selling hand sanitizers is $1.5 \cdot x_2$. The objective is to maximize the daily profit, which can be represented as:
\[ \text{Maximize:} \quad 1x_1 + 1.5x_2 \]

## 3: Translate the constraints into symbolic notation
The constraints given are:
- The budget constraint: $1.5x_1 + 3x_2 \leq 1000$
- The face mask sales constraint: $80 \leq x_1 \leq 500$
- The hand sanitizer sales constraint: $x_2 \leq 0.5x_1$

## 4: Compile the symbolic representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x1', 'face masks'), ('x2', 'hand sanitizers')],
'objective_function': 'Maximize: 1*x1 + 1.5*x2',
'constraints': [
    '1.5*x1 + 3*x2 <= 1000',
    '80 <= x1 <= 500',
    'x2 <= 0.5*x1'
]
}
```

## 5: Convert the problem into Gurobi code
Now, let's convert this problem into Gurobi code in Python:
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=80, ub=500, name="face_masks")  # face masks
    x2 = model.addVar(name="hand_sanitizers")  # hand sanitizers

    # Objective function: Maximize 1*x1 + 1.5*x2
    model.setObjective(1*x1 + 1.5*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(1.5*x1 + 3*x2 <= 1000, name="budget_constraint")
    model.addConstr(x2 <= 0.5*x1, name="hand_sanitizer_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Face masks: {x1.varValue}")
        print(f"Hand sanitizers: {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```