## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The smoothie store wants to maximize its profit by selling small and large smoothies, given the constraints on the available ice cream and peanut butter.

Let's define the decision variables:

* `x`: number of small smoothies to sell
* `y`: number of large smoothies to sell

The objective function is to maximize the profit:

* Profit per small smoothie: $3
* Profit per large smoothie: $5
* Total profit: `3x + 5y`

The constraints are:

* Ice cream: 2 units per small smoothie, 3 units per large smoothie, total available: 20 units
* `2x + 3y <= 20`
* Peanut butter: 1 unit per small smoothie, 2 units per large smoothie, total available: 18 units
* `x + 2y <= 18`
* Non-negativity constraints: `x >= 0`, `y >= 0`

## Gurobi Code

```python
import gurobi

# Create a new Gurobi model
m = gurobi.Model()

# Define the decision variables
x = m.addVar(lb=0, name="small_smoothies")
y = m.addVar(lb=0, name="large_smoothies")

# Define the objective function
m.setObjective(3*x + 5*y, gurobi.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(2*x + 3*y <= 20, name="ice_cream_constraint")
m.addConstr(x + 2*y <= 18, name="peanut_butter_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Small smoothies: {x.varValue}")
    print(f"Large smoothies: {y.varValue}")
    print(f"Max profit: {m.objVal}")
else:
    print("No optimal solution found.")
```

This code defines the decision variables, objective function, and constraints, and then solves the model using Gurobi's optimization algorithm. If an optimal solution is found, it prints the number of small and large smoothies to sell and the maximum profit. Otherwise, it indicates that no optimal solution was found.