## Problem Description and Symbolic Representation

The problem can be broken down into the following components:

- **Variables:**
  - Let \(x_1\) be the number of t-shirts.
  - Let \(x_2\) be the number of hoodies.

- **Objective Function:**
  - The profit from \(x_1\) t-shirts is $10\(x_1\).
  - The profit from \(x_2\) hoodies is $15\(x_2\).
  - Therefore, the total profit \(P\) to be maximized is: \(P = 10x_1 + 15x_2\).

- **Constraints:**
  - Designing time: \(x_1 + 2x_2 \leq 40\) (since t-shirts require 1 hour and hoodies require 2 hours of designing time, and there are 40 hours available).
  - Printing time: \(2x_1 + 3x_2 \leq 60\) (since t-shirts require 2 hours and hoodies require 3 hours of printing time, and there are 60 hours available).
  - Non-negativity: \(x_1 \geq 0, x_2 \geq 0\) (as the number of t-shirts and hoodies cannot be negative).

## Symbolic Representation in JSON Format

```json
{
  'sym_variables': [('x1', 't-shirts'), ('x2', 'hoodies')],
  'objective_function': '10*x1 + 15*x2',
  'constraints': [
    'x1 + 2*x2 <= 40',
    '2*x1 + 3*x2 <= 60',
    'x1 >= 0',
    'x2 >= 0'
  ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="t-shirts", lb=0, vtype=gp.GRB.CONTINUOUS)
x2 = model.addVar(name="hoodies", lb=0, vtype=gp.GRB.CONTINUOUS)

# Objective function
model.setObjective(10*x1 + 15*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 + 2*x2 <= 40, name="designing_time")
model.addConstr(2*x1 + 3*x2 <= 60, name="printing_time")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
  print("Optimal Solution:")
  print(f"t-shirts: {x1.varValue}")
  print(f"hoodies: {x2.varValue}")
  print(f"Max Profit: {model.objVal}")
else:
  print("The model is infeasible.")
```