## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to maximize the profit of a fast food restaurant by determining the optimal number of cheeseburgers (x1) and fries (x2) to produce daily.

### Objective Function

The profit from x1 cheeseburgers is $1.50x1, and the profit from x2 fries is $1x2. The total profit (P) to be maximized is:

P = 1.50x1 + x2

### Constraints

1. **Non-negativity constraints**: x1 ≥ 0 and x2 ≥ 0, as the number of cheeseburgers and fries produced cannot be negative.
2. **Demand constraints**: The restaurant has a daily demand for at most 110 cheeseburgers and 80 fries. This translates to:
   - x1 ≤ 110
   - x2 ≤ 80
3. **Capacity constraint**: The restaurant can make a maximum of 150 items of either type. This translates to:
   - x1 + x2 ≤ 150

## Gurobi Code

To solve this problem using Gurobi in Python, we can use the following code:

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(lb=0, name="x1")  # Number of cheeseburgers
    x2 = model.addVar(lb=0, name="x2")  # Number of fries

    # Objective function: Maximize profit
    model.setObjective(1.50 * x1 + x2, gurobi.GRB.MAXIMIZE)

    # Demand constraints
    model.addConstr(x1 <= 110, name="cheeseburger_demand")
    model.addConstr(x2 <= 80, name="fries_demand")

    # Capacity constraint
    model.addConstr(x1 + x2 <= 150, name="production_capacity")

    # Optimize
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Cheeseburgers (x1): {x1.varValue}")
        print(f"Fries (x2): {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("The model is infeasible.")

solve_optimization_problem()
```

This code defines the optimization problem using Gurobi's Python interface, solves it, and prints out the optimal production levels for cheeseburgers and fries, along with the maximum achievable profit. If the problem is infeasible, it indicates so.