## Symbolic Representation

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

Let's define the symbolic variables as follows:

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

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

Maximize: $4x_1 + 5x_2$

The constraints based on the problem description are:

1. $x_1 \geq 35$ (at least 35 pepperoni pizzas must be sold)
2. $x_1 \leq 40$ (no more than 40 pepperoni pizzas can be sold)
3. $x_2 \geq 40$ (at least 40 Hawaiian pizzas must be sold)
4. $x_2 \leq 70$ (no more than 70 Hawaiian pizzas can be sold)
5. $x_1 + x_2 \leq 90$ (total pizzas sold cannot exceed 90)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'pepperoni pizzas'), ('x2', 'Hawaiian pizzas')],
    'objective_function': '4*x1 + 5*x2',
    'constraints': [
        'x1 >= 35',
        'x1 <= 40',
        'x2 >= 40',
        'x2 <= 70',
        'x1 + x2 <= 90'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
m = gp.Model("pizza_shop")

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

# Objective function: Maximize profit
m.setObjective(4*x1 + 5*x2, gp.GRB.MAXIMIZE)

# Constraint: Total pizzas cannot exceed 90
m.addConstraint(x1 + x2 <= 90)

# Solve the model
m.solve()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Pepperoni Pizzas: {x1.varValue}")
    print(f"Hawaiian Pizzas: {x2.varValue}")
    print(f"Max Profit: {m.objVal}")
else:
    print("No optimal solution found.")
```