## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The goal is to maximize the profit of a food truck by determining the optimal number of apple and orange smoothies to produce, given the constraints on the availability of the cutting and blending machines.

Let's define the decision variables:

* $x$: the number of apple smoothies to produce
* $y$: the number of orange smoothies to produce

The objective function is to maximize the profit:

* Profit per apple smoothie: $3.5
* Profit per orange smoothie: $4.5
* Total profit: $3.5x + 4.5y

The constraints are:

* Cutting machine availability: $6x + 5y \leq 500$
* Blending machine availability: $3x + 2y \leq 500$
* Non-negativity constraints: $x \geq 0, y \geq 0$

## Gurobi Code

```python
import gurobi

def solve_smoothie_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define the decision variables
    x = model.addVar(name="apple_smoothies", lb=0, ub=gurobi.GRB.INFINITY)
    y = model.addVar(name="orange_smoothies", lb=0, ub=gurobi.GRB.INFINITY)

    # Define the objective function
    model.setObjective(3.5 * x + 4.5 * y, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(6 * x + 5 * y <= 500, name="cutting_machine")
    model.addConstr(3 * x + 2 * y <= 500, name="blending_machine")

    # Optimize the model
    model.optimize()

    # Check if the model is infeasible
    if model.status == gurobi.GRB.Status.INFEASIBLE:
        print("The problem is infeasible")
        return

    # Print the solution
    print("Optimal solution:")
    print(f"Apple smoothies: {x.varValue}")
    print(f"Orange smoothies: {y.varValue}")
    print(f"Max profit: {model.objVal}")

solve_smoothie_problem()
```