## Step 1: Define the symbolic representation of the problem

Let's denote the number of small gifts wrapped as $x_1$ and the number of large gifts wrapped as $x_2$. The objective is to maximize profit, where the profit per small gift is $3 and per large gift is $5. Therefore, the objective function can be represented as $3x_1 + 5x_2$.

## Step 2: Identify the constraints

The kiosk has limited worker time and wrapping paper. Small gifts take 10 minutes of worker time, and large gifts take 15 minutes. With 720 minutes available, the worker time constraint can be represented as $10x_1 + 15x_2 \leq 720$. For wrapping paper, small gifts take 2 units and large gifts take 3 units, with 150 units available, leading to the constraint $2x_1 + 3x_2 \leq 150$. Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of gifts cannot be negative.

## 3: Symbolic representation in the required format

The symbolic variables are:
- $x_1$ for small gifts
- $x_2$ for large gifts

The objective function is: $3x_1 + 5x_2$

The constraints are:
- $10x_1 + 15x_2 \leq 720$
- $2x_1 + 3x_2 \leq 150$
- $x_1 \geq 0$
- $x_2 \geq 0$

In the required format:
```json
{
'sym_variables': [('x1', 'small gifts'), ('x2', 'large gifts')],
'objective_function': '3*x1 + 5*x2',
'constraints': ['10*x1 + 15*x2 <= 720', '2*x1 + 3*x2 <= 150', 'x1 >= 0', 'x2 >= 0']
}
```

## 4: Convert the problem into Gurobi code

To solve this linear programming problem using Gurobi, we will use the Gurobi Python interface.

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='x1', lb=0, ub=gurobi.GRB.INFINITY, obj=3)  # small gifts
    x2 = model.addVar(name='x2', lb=0, ub=gurobi.GRB.INFINITY, obj=5)  # large gifts

    # Add constraints
    model.addConstr(x1 * 10 + x2 * 15 <= 720, name='worker_time')
    model.addConstr(x1 * 2 + x2 * 3 <= 150, name='wrapping_paper')

    # Set the objective function
    model.setObjective(x1 * 3 + x2 * 5, gurobi.GRB.MAXIMIZE)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Maximum profit: ${3*x1.varValue + 5*x2.varValue:.2f}")
    else:
        print("The model is infeasible.")

solve_gift_wrapping_problem()
```