To solve the given optimization problem, we first need to understand and translate the natural language description into a mathematical model. The objective is to maximize profit from producing cheeseburgers and fries under certain constraints.

Let's denote:
- \(x_1\) as the number of cheeseburgers produced per day.
- \(x_2\) as the number of fries produced per day.

The profit per cheeseburger (\(x_1\)) is $1.50, and the profit per serving of fries (\(x_2\)) is $1.00.

Given constraints:
1. Non-negativity: \(x_1 \geq 0\) and \(x_2 \geq 0\), as the production cannot be negative.
2. Demand constraint for cheeseburgers: \(x_1 \leq 110\).
3. Demand constraint for fries: \(x_2 \leq 80\).
4. Total capacity constraint: \(x_1 + x_2 \leq 150\), as the restaurant can produce a maximum of 150 items per day.

The objective function to maximize profit (\(P\)) is:
\[ P = 1.50x_1 + 1.00x_2 \]

Now, let's translate this problem into Gurobi code in Python:

```python
from gurobipy import *

# Create a model
m = Model("FastFoodOptimization")

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Cheeseburgers")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Fries")

# Set objective function: Maximize profit
m.setObjective(1.50*x1 + 1.00*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 <= 110, "Demand_Cheeseburgers")
m.addConstr(x2 <= 80, "Demand_Fries")
m.addConstr(x1 + x2 <= 150, "Total_Capacity")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Produce {x1.x} cheeseburgers")
    print(f"Produce {x2.x} fries")
    print(f"Maximum Profit: ${m.objVal}")
else:
    print("No optimal solution found")

```