## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The auto plant wants to maximize its profit by producing a certain number of cars and trucks, given the constraints on assembly line time and mechanic time.

Let's define the decision variables:

* `c`: number of cars to produce
* `t`: number of trucks to produce

The objective function is to maximize the total profit:

* Profit per car: $5000
* Profit per truck: $8000
* Total profit: `5000c + 8000t`

The constraints are:

* Assembly line time: `2c + 2.5t <= 800`
* Mechanic time: `c + 1.5t <= 600`
* Non-negativity constraints: `c >= 0`, `t >= 0`

## Gurobi Code

```python
import gurobi

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

# Define the decision variables
c = model.addVar(lb=0, name="cars")
t = model.addVar(lb=0, name="trucks")

# Define the objective function
model.setObjective(5000 * c + 8000 * t, gurobi.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(2 * c + 2.5 * t <= 800, name="assembly_line_time")
model.addConstr(c + 1.5 * t <= 600, name="mechanic_time")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Cars to produce: {c.varValue}")
    print(f"Trucks to produce: {t.varValue}")
    print(f"Maximum profit: {model.objVal}")
else:
    print("No optimal solution found.")
```

This code defines the decision variables, objective function, and constraints, and then solves the model using Gurobi's optimization algorithm. If an optimal solution is found, it prints the number of cars and trucks to produce and the maximum profit. Otherwise, it indicates that no optimal solution was found.