To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of pepperoni pizzas sold,
- $x_2$ as the number of Hawaiian pizzas sold.

The objective function aims to maximize profit. Given that the profit per pepperoni pizza is $4 and per Hawaiian pizza is $5, the objective function can be represented algebraically as:

$$\text{Maximize: } 4x_1 + 5x_2$$

The constraints based on the problem description are:
1. The shop must sell at least 35 pepperoni pizzas but cannot sell more than 40.
   - $35 \leq x_1 \leq 40$
2. They must sell at least 40 Hawaiian pizzas but cannot sell more than 70.
   - $40 \leq x_2 \leq 70$
3. In total, they only have enough supplies to sell 90 pizzas.
   - $x_1 + x_2 \leq 90$

Thus, the symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'number of pepperoni pizzas sold'), ('x2', 'number of Hawaiian pizzas sold')],
  'objective_function': '4*x1 + 5*x2',
  'constraints': ['35 <= x1 <= 40', '40 <= x2 <= 70', 'x1 + x2 <= 90']
}
```

To solve this problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=35, ub=40, vtype=GRB.INTEGER, name="pepperoni_pizzas")
x2 = m.addVar(lb=40, ub=70, vtype=GRB.INTEGER, name="hawaiian_pizzas")

# Set the objective function
m.setObjective(4*x1 + 5*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 90, name="total_pizzas")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Pepperoni pizzas to sell: {x1.x}")
    print(f"Hawaiian pizzas to sell: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```