To solve the optimization problem described, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the given information.

Let's denote:
- \(x_1\) as the number of superhero costumes made,
- \(x_2\) as the number of fantasy costumes made.

The objective is to maximize the total profit. Given that the profit per superhero costume is $24 and the profit per fantasy costume is $32, the objective function can be written as:
\[ \text{Maximize: } 24x_1 + 32x_2 \]

Now, let's consider the constraints:
1. **Time Constraint**: It takes 20 minutes to make a superhero costume and 15 minutes to make a fantasy costume, with a total of 3000 minutes available.
   - \(20x_1 + 15x_2 \leq 3000\)
2. **Market Research Constraint**: The company should make at least 3 times as many fantasy costumes as superhero costumes.
   - \(x_2 \geq 3x_1\)
3. **Non-Negativity Constraints**: Since the number of costumes cannot be negative, we have:
   - \(x_1 \geq 0\)
   - \(x_2 \geq 0\)

Thus, our symbolic representation in JSON format is:

```json
{
    'sym_variables': [('x1', 'number of superhero costumes'), ('x2', 'number of fantasy costumes')],
    'objective_function': '24*x1 + 32*x2',
    'constraints': [
        '20*x1 + 15*x2 <= 3000',
        'x2 >= 3*x1',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

To solve this problem using Gurobi in Python, we'll use the following code:

```python
from gurobipy import *

# Create a new model
m = Model("Costume_Production")

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

# Set the objective function
m.setObjective(24*x1 + 32*x2, GRB.MAXIMIZE)

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

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of superhero costumes: {x1.x}")
    print(f"Number of fantasy costumes: {x2.x}")
    print(f"Total profit: ${24*x1.x + 32*x2.x:.2f}")
else:
    print("No optimal solution found")
```