To solve the problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables for the quantities of each type of pot John should make, formulating the objective function that represents the total profit, and listing the constraints based on the available time for shaping and baking.

Let's define:
- \(x_1\) as the number of oval pots,
- \(x_2\) as the number of square pots.

The profit per oval pot is $4.5, and the profit per square pot is $8. Thus, the objective function to maximize the total profit can be represented as:
\[ \text{Maximize:} \quad 4.5x_1 + 8x_2 \]

The constraints are based on the available time for shaping and baking. Each oval pot requires 40 minutes of shaping time and 50 minutes of baking time, while each square pot requires 35 minutes of shaping time and 80 minutes of baking time. The total available time per week is 2500 minutes for shaping and 3800 minutes for baking. Therefore, the constraints can be represented as:
\[ 40x_1 + 35x_2 \leq 2500 \] (shaping time constraint)
\[ 50x_1 + 80x_2 \leq 3800 \] (baking time constraint)

Also, \(x_1 \geq 0\) and \(x_2 \geq 0\), since John cannot make a negative number of pots.

In symbolic representation with natural language objects:
```json
{
  'sym_variables': [('x1', 'number of oval pots'), ('x2', 'number of square pots')],
  'objective_function': '4.5*x1 + 8*x2',
  'constraints': ['40*x1 + 35*x2 <= 2500', '50*x1 + 80*x2 <= 3800', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this linear programming problem using Gurobi in Python, we can use the following code:
```python
from gurobipy import *

# Create a new model
m = Model("Terracotta_Pots")

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="oval_pots", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="square_pots", lb=0)

# Set the objective function
m.setObjective(4.5*x1 + 8*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(40*x1 + 35*x2 <= 2500, "shaping_time")
m.addConstr(50*x1 + 80*x2 <= 3800, "baking_time")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of oval pots: {x1.x}")
    print(f"Number of square pots: {x2.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```