To solve Pierre's optimization problem, we first need to translate the natural language description into a symbolic representation. Let's define:

- $x_1$ as the number of sandals to buy,
- $x_2$ as the number of slippers to buy.

The objective is to maximize profit. Given that the profit per sandal sold is $70 and the profit per slipper sold is $30, we can represent the total profit (objective function) as:

\[ 70x_1 + 30x_2 \]

The constraints based on the problem description are:
1. The demand for sandals is at least three times the demand for slippers: \( x_1 \geq 3x_2 \).
2. Pierre decides to invest at most $3000 buying for his first inventory, with sandals costing $50 and slippers costing $20: \( 50x_1 + 20x_2 \leq 3000 \).
3. Non-negativity constraints since the number of items cannot be negative: \( x_1 \geq 0 \) and \( x_2 \geq 0 \).

Thus, the symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'number of sandals'), ('x2', 'number of slippers')],
    'objective_function': '70*x1 + 30*x2',
    'constraints': ['x1 >= 3*x2', '50*x1 + 20*x2 <= 3000', 'x1 >= 0', 'x2 >= 0']
}
```

Here's how we can implement this problem in Gurobi using Python:
```python
from gurobipy import *

# Create a new model
m = Model("Pierre_e-commerce")

# Define the variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="sandals")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="slippers")

# Set the objective function
m.setObjective(70*x1 + 30*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 >= 3*x2, "demand_ratio")
m.addConstr(50*x1 + 20*x2 <= 3000, "budget_constraint")
m.addConstr(x1 >= 0, "non_neg_sandals")
m.addConstr(x2 >= 0, "non_neg_slippers")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of sandals: {x1.x}")
    print(f"Number of slippers: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```