## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to maximize the profit of a snow removal company by determining the amount of snow to be removed in two cities, given the constraints on the availability of equipment.

### Variables

- $x_n$: kilograms of snow to be removed in the northern city
- $x_s$: kilograms of snow to be removed in the southern city

### Objective Function

The objective is to maximize profit. The net revenue per kilogram of snow is $2 in the northern city and $1.50 in the southern city.

- Maximize: $2x_n + 1.5x_s$

### Constraints

- Each item of equipment can be used for at most 500 minutes per day.
- At the northern city, to remove 1 kilogram of snow requires 2 minutes on the snow plow, 1 minute on the truck, and 5 minutes with the shovel.
- At the southern city, to remove 1 kilogram of snow requires 1 minute on the snow plow, 3 minutes on the truck, and 2 minutes with the shovel.

### Constraints Formulation

- Snow plow constraint: $2x_n + x_s \leq 500$
- Truck constraint: $x_n + 3x_s \leq 500$
- Shovel constraint: $5x_n + 2x_s \leq 500$
- Non-negativity constraints: $x_n \geq 0, x_s \geq 0$

## Gurobi Code

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Snow_Removal")

# Variables
x_n = model.addVar(name="x_n", lb=0, ub=gp.GRB.INFINITY)  # kilograms of snow in the northern city
x_s = model.addVar(name="x_s", lb=0, ub=gp.GRB.INFINITY)  # kilograms of snow in the southern city

# Objective function
model.setObjective(2 * x_n + 1.5 * x_s, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(2 * x_n + x_s <= 500, name="snow_plow_constraint")
model.addConstr(x_n + 3 * x_s <= 500, name="truck_constraint")
model.addConstr(5 * x_n + 2 * x_s <= 500, name="shovel_constraint")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: x_n = {x_n.varValue}, x_s = {x_s.varValue}")
    print(f"Maximum profit: {model.objVal}")
else:
    print("The model is infeasible")
```