## Symbolic Representation

To solve George's problem of maximizing profit from buying and selling sneakers and boots, we first need to convert the natural language description into a symbolic representation.

Let's denote:
- \(x_1\) as the number of sneakers George buys
- \(x_2\) as the number of boots George buys

The objective is to maximize profit. Given that the profit per sneaker sold is $50 and per boot sold is $80, the objective function can be represented as:
\[ \text{Maximize:} \quad 50x_1 + 80x_2 \]

The constraints are:
1. The monthly demand for each type of shoe is at most 50.
\[ x_1 \leq 50 \]
\[ x_2 \leq 50 \]

2. George does not want to spend more than $8750, with sneakers costing $150 each and boots costing $200 each.
\[ 150x_1 + 200x_2 \leq 8750 \]

3. Non-negativity constraints, as George cannot buy a negative number of shoes.
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'sneakers'), ('x2', 'boots')],
    'objective_function': '50*x1 + 80*x2',
    'constraints': [
        'x1 <= 50',
        'x2 <= 50',
        '150*x1 + 200*x2 <= 8750',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

def solve_george_problem():
    # Create a new model
    model = gp.Model("George's Problem")

    # Define variables
    x1 = model.addVar(name="sneakers", lb=0, ub=50, vtype=gp.GRB.INTEGER)
    x2 = model.addVar(name="boots", lb=0, ub=50, vtype=gp.GRB.INTEGER)

    # Objective function: Maximize 50*x1 + 80*x2
    model.setObjective(50*x1 + 80*x2, gp.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 <= 50, name="demand_sneakers")
    model.addConstr(x2 <= 50, name="demand_boots")
    model.addConstr(150*x1 + 200*x2 <= 8750, name="budget_constraint")

    # Solve the model
    model.optimize()

    # Print solution
    if model.status == gp.GRB.OPTIMAL:
        print(f"Optimal solution: Buy {x1.varValue} sneakers and {x2.varValue} boots.")
    else:
        print("No optimal solution found.")

solve_george_problem()
```