## Problem Description and Formulation

The food truck optimization problem can be formulated as a linear programming problem. The goal is to maximize profit given certain constraints on the number of orders of fries and onion rings that can be sold.

### Decision Variables

- \(x\): Number of orders of fries to sell
- \(y\): Number of orders of onion rings to sell

### Objective Function

The profit per order of fries is $4, and the profit per order of onion rings is $5. The objective is to maximize the total profit \(P\), which can be represented as:
\[ P = 4x + 5y \]

### Constraints

1. **Fries Sales Constraints**: The food truck must sell at least 20 orders of fries but can make at most 50 orders.
\[ 20 \leq x \leq 50 \]

2. **Onion Rings Sales Constraints**: They must sell at least 10 orders of onion rings but can make at most 40 orders.
\[ 10 \leq y \leq 40 \]

3. **Total Orders Constraint**: Due to limited fryer time, the food truck can only sell 50 orders total.
\[ x + y \leq 50 \]

4. **Non-Negativity Constraints**: Since the number of orders cannot be negative, we have:
\[ x \geq 0, y \geq 0 \]
However, these are partially covered by the lower bounds of \(x\) and \(y\).

## Gurobi Code Formulation

Given the formulation above, we can now translate this into Gurobi code in Python:

```python
import gurobi

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

    # Define variables with their bounds
    x = model.addVar(lb=20, ub=50, name="fries")
    y = model.addVar(lb=10, ub=40, name="onion_rings")

    # Objective function: Maximize profit
    model.setObjective(4*x + 5*y, gurobi.GRB.MAXIMIZE)

    # Constraint: Total orders cannot exceed 50
    model.addConstr(x + y <= 50, name="total_orders")

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal Solution: x = {x.varValue}, y = {y.varValue}")
        print(f"Maximum Profit: ${4*x.varValue + 5*y.varValue}")
    else:
        print("The model is infeasible.")

solve_food_truck_problem()
```

This code defines a linear programming problem with Gurobi, where the goal is to maximize profit under the given constraints. It then solves the problem and prints out the optimal number of orders for fries and onion rings, along with the maximum achievable profit.