## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of superhero costumes.
- $x_2$ represents the number of fantasy costumes.

## Step 2: Formulate the objective function
The profit per superhero costume is $24, and the profit per fantasy costume is $32. The objective function to maximize the total profit is:
\[ \text{Maximize:} \quad 24x_1 + 32x_2 \]

## 3: Define the constraints
Based on the problem description, we have the following constraints:
1. It takes 20 minutes to make a superhero costume and 15 minutes to make a fantasy costume, with 3000 minutes available:
\[ 20x_1 + 15x_2 \leq 3000 \]
2. The company should make at least 3 times as many fantasy costumes as superhero costumes:
\[ x_2 \geq 3x_1 \]
3. Non-negativity constraints (number of costumes cannot be negative):
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

## 4: Symbolic representation of the problem
The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'superhero costumes'), ('x2', 'fantasy costumes')],
    'objective_function': '24*x1 + 32*x2',
    'constraints': [
        '20*x1 + 15*x2 <= 3000',
        'x2 >= 3*x1',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Gurobi code
Now, let's write the Gurobi code in Python to solve this problem:
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="superhero_costumes", lb=0, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="fantasy_costumes", lb=0, vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(24 * x1 + 32 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(20 * x1 + 15 * x2 <= 3000, name="time_constraint")
    model.addConstr(x2 >= 3 * x1, name="ratio_constraint")

    # 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: ${24 * x1.varValue + 32 * x2.varValue}")
    else:
        print("No optimal solution found.")

solve_party_supplies_problem()
```