## Problem Description and Symbolic Representation

The problem involves a leather shop that produces wallets and purses. The goal is to maximize profit given the time constraints for cutting and stitching.

### Symbolic Representation:

Let's denote:
- $x_1$ as the number of wallets
- $x_2$ as the number of purses

The profit per wallet is $50, and the profit per purse is $100. Therefore, the objective function to maximize profit ($P$) is:
\[ P = 50x_1 + 100x_2 \]

The constraints based on the available time for cutting and stitching are:
- Cutting time: $10x_1 + 15x_2 \leq 500$
- Stitching time: $20x_1 + 30x_2 \leq 600$

Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of wallets and purses cannot be negative.

### Symbolic Representation in JSON Format:

```json
{
    'sym_variables': [('x1', 'wallets'), ('x2', 'purses')],
    'objective_function': '50*x1 + 100*x2',
    'constraints': [
        '10*x1 + 15*x2 <= 500',
        '20*x1 + 30*x2 <= 600',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="wallets", lb=0, vtype=gp.GRB.INTEGER)  # Number of wallets
x2 = model.addVar(name="purses", lb=0, vtype=gp.GRB.INTEGER)   # Number of purses

# Objective function: Maximize profit
model.setObjective(50*x1 + 100*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(10*x1 + 15*x2 <= 500, name="cutting_time")
model.addConstr(20*x1 + 30*x2 <= 600, name="stitching_time")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: {model.getVarByName('wallets').varName} = {model.getVarByName('wallets').x}, {model.getVarByName('purses').varName} = {model.getVarByName('purses').x}")
    print(f"Max Profit: ${model.objVal}")
else:
    print("No optimal solution found")
```