## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, as well as the constraints.

### Variables
- $x_1$: Hours of operation for the mall kiosk
- $x_2$: Hours of operation for the flagship store

### Objective Function
The objective is to minimize the total cost of operating the mall kiosk and the flagship store. The cost to operate the mall kiosk is $150 per hour, and the cost to operate the flagship store is $500 per hour. Therefore, the objective function can be represented as:
\[ \text{Minimize:} \quad 150x_1 + 500x_2 \]

### Constraints
1. **Small Gift Boxes:** The company must make a minimum of 80 small gift boxes per day. The mall kiosk can make 5 small gift boxes per hour, and the flagship store can make 10 small gift boxes per hour.
\[ 5x_1 + 10x_2 \geq 80 \]

2. **Medium Gift Boxes:** The company must make a minimum of 100 medium gift boxes per day. The mall kiosk can make 6 medium gift boxes per hour, and the flagship store can make 15 medium gift boxes per hour.
\[ 6x_1 + 15x_2 \geq 100 \]

3. **Large Gift Boxes:** The company must make a minimum of 50 large gift boxes per day. The mall kiosk can make 2 large gift boxes per hour, and the flagship store can make 9 large gift boxes per hour.
\[ 2x_1 + 9x_2 \geq 50 \]

4. **Non-Negativity Constraints:** The hours of operation cannot be negative.
\[ x_1 \geq 0, x_2 \geq 0 \]

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'mall kiosk hours'), ('x2', 'flagship store hours')],
    'objective_function': '150*x1 + 500*x2',
    'constraints': [
        '5*x1 + 10*x2 >= 80',
        '6*x1 + 15*x2 >= 100',
        '2*x1 + 9*x2 >= 50',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="mall_kiosk_hours", lb=0)  # Hours of operation for the mall kiosk
x2 = model.addVar(name="flagship_store_hours", lb=0)  # Hours of operation for the flagship store

# Objective function: Minimize cost
model.setObjective(150 * x1 + 500 * x2, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(5 * x1 + 10 * x2 >= 80, name="small_gift_boxes")  # Small gift boxes constraint
model.addConstr(6 * x1 + 15 * x2 >= 100, name="medium_gift_boxes")  # Medium gift boxes constraint
model.addConstr(2 * x1 + 9 * x2 >= 50, name="large_gift_boxes")  # Large gift boxes constraint

# Solve the model
model.solve()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Mall Kiosk Hours: {x1.varValue}")
    print(f"Flagship Store Hours: {x2.varValue}")
    print(f"Total Cost: {model.objVal}")
else:
    print("No optimal solution found.")
```