## 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:

- $x_1$ : Number of peanut butter sandwiches
- $x_2$ : Number of chocolate spread sandwiches

The objective is to maximize profit. The profit per peanut butter sandwich is $3, and the profit per chocolate spread sandwich is $2. Therefore, the objective function can be represented as:

Maximize $3x_1 + 2x_2$

The constraints based on the given information are:

1. The store only has enough bread to make at most 150 sandwiches: $x_1 + x_2 \leq 150$
2. The store must sell at least 45 peanut butter sandwiches: $x_1 \geq 45$
3. The store must sell at least 65 chocolate spread sandwiches: $x_2 \geq 65$
4. The store only has enough spread, peanut butter, and chocolate to make at most 80 peanut butter sandwiches: $x_1 \leq 80$
5. The store only has enough spread, peanut butter, and chocolate to make at most 100 chocolate spread sandwiches: $x_2 \leq 100$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'peanut butter sandwiches'), ('x2', 'chocolate spread sandwiches')],
    'objective_function': '3*x1 + 2*x2',
    'constraints': [
        'x1 + x2 <= 150',
        'x1 >= 45',
        'x2 >= 65',
        'x1 <= 80',
        'x2 <= 100'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = m.addVar(name="peanut_butter_sandwiches", lb=0, ub=gp.GRB.INFINITY)
x2 = m.addVar(name="chocolate_spread_sandwiches", lb=0, ub=gp.GRB.INFINITY)

# Objective function: Maximize 3*x1 + 2*x2
m.setObjective(3*x1 + 2*x2, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(x1 + x2 <= 150, name="total_sandwiches")
m.addConstr(x1 >= 45, name="min_peanut_butter")
m.addConstr(x2 >= 65, name="min_chocolate_spread")
m.addConstr(x1 <= 80, name="max_peanut_butter")
m.addConstr(x2 <= 100, name="max_chocolate_spread")

# Solve the model
m.solve()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Peanut Butter Sandwiches: {x1.varValue}")
    print(f"Chocolate Spread Sandwiches: {x2.varValue}")
    print(f"Max Profit: {m.objVal}")
else:
    print("The model is infeasible or unbounded.")
```