## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The goal is to maximize the profit of a printing company by determining the optimal number of books and magazines to print, given the constraints on printing and binding time.

Let's define the decision variables:

* `B`: the number of books to print
* `M`: the number of magazines to print

The objective function is to maximize the total profit:

* Profit per book: $5
* Profit per magazine: $8
* Total profit: `5B + 8M`

The constraints are:

* Printing time: 10 minutes per book, 20 minutes per magazine, and 5000 minutes available
* Binding time: 5 minutes per book, 3 minutes per magazine, and 2000 minutes available

## Mathematical Formulation

The mathematical formulation of the problem is:

Maximize: `5B + 8M`

Subject to:

* `10B + 20M <= 5000` (printing time constraint)
* `5B + 3M <= 2000` (binding time constraint)
* `B >= 0` and `M >= 0` (non-negativity constraints)

## Gurobi Code

```python
import gurobi

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

# Define the decision variables
B = m.addVar(lb=0, name="Books")
M = m.addVar(lb=0, name="Magazines")

# Define the objective function
m.setObjective(5*B + 8*M, gurobi.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(10*B + 20*M <= 5000, name="Printing_Time")
m.addConstr(5*B + 3*M <= 2000, name="Binding_Time")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Number of books to print: {B.varValue}")
    print(f"Number of magazines to print: {M.varValue}")
    print(f"Maximum profit: ${m.objVal:.2f}")
else:
    print("No optimal solution found.")
```