## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The goal is to maximize the profit of XYZ Automobile by determining the optimal number of SUV cars and minivans to produce.

Let's define the decision variables:

* `suv`: number of SUV cars produced per day
* `minivan`: number of minivans produced per day

The objective function is to maximize the profit:

* Profit per SUV car: $7500
* Profit per minivan: $4000

The constraints are:

* The SUV car factory can make at most 5 SUV cars per day: `suv <= 5`
* The minivan car factory can make at most 3 minivans per day: `minivan <= 3`
* The third-party finishing touches facility can process at most 5 vehicles of either type per day: `suv + minivan <= 5`
* Non-negativity constraints: `suv >= 0`, `minivan >= 0`

## Gurobi Code

```python
import gurobi

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

# Define the decision variables
suv = model.addVar(lb=0, ub=5, name="suv", vtype=gurobi.GRB.CONTINUOUS)
minivan = model.addVar(lb=0, ub=3, name="minivan", vtype=gurobi.GRB.CONTINUOUS)

# Define the objective function
model.setObjective(7500 * suv + 4000 * minivan, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(suv <= 5, name="suv_constraint")
model.addConstr(minivan <= 3, name="minivan_constraint")
model.addConstr(suv + minivan <= 5, name="finishing_constraint")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"SUV cars: {suv.x:.2f}")
    print(f"Minivans: {minivan.x:.2f}")
    print(f"Max Profit: {model.objVal:.2f}")
else:
    print("No optimal solution found.")
```