## Problem Description and Symbolic Representation

Let's denote the number of sandals and slippers as $x_1$ and $x_2$ respectively.

The objective is to maximize the profit, which is $70x_1 + 30x_2$.

The constraints are:
1. The demand for sandals is at least three times the demand for slippers: $x_1 \geq 3x_2$.
2. The total investment is at most $3000: $50x_1 + 20x_2 \leq 3000$.
3. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$.

## Symbolic Representation

```json
{
    'sym_variables': [('x1', 'sandals'), ('x2', 'slippers')],
    'objective_function': '70*x1 + 30*x2',
    'constraints': [
        'x1 >= 3*x2',
        '50*x1 + 20*x2 <= 3000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name='sandals', lb=0, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='slippers', lb=0, vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(70*x1 + 30*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 >= 3*x2, name='demand_constraint')
    model.addConstr(50*x1 + 20*x2 <= 3000, name='investment_constraint')

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: sandals = {x1.varValue}, slippers = {x2.varValue}")
        print(f"Max profit: {model.objVal}")
    else:
        print("No optimal solution found")

solve_pierre_problem()
```