## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The factory produces two types of paper: dotted paper and grid paper. Each type of paper requires a certain amount of time on two machines: a cutting machine and a printing machine. The goal is to maximize the profit by determining the optimal number of reams of each type of paper to produce.

Let's define the variables:

* $x$: number of reams of dotted paper to produce
* $y$: number of reams of grid paper to produce

The objective function is to maximize the profit:

* Profit per ream of dotted paper: $5.5
* Profit per ream of grid paper: $11
* Total profit: $5.5x + 11y$

The constraints are:

* Cutting machine availability: $3x + 1.5y \leq 3000$
* Printing machine availability: $5.5x + 7y \leq 3000$
* Non-negativity constraints: $x \geq 0, y \geq 0$

## Gurobi Code

```python
import gurobi

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

# Define the variables
x = model.addVar(lb=0, name="dotted_paper")
y = model.addVar(lb=0, name="grid_paper")

# Define the objective function
model.setObjective(5.5 * x + 11 * y, gurobi.GRB.MAXIMIZE)

# Define the constraints
cutting_machine_constraint = model.addConstr(3 * x + 1.5 * y <= 3000, name="cutting_machine")
printing_machine_constraint = model.addConstr(5.5 * x + 7 * y <= 3000, name="printing_machine")

# Optimize the model
model.optimize()

# Print the results
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Dotted paper: {x.varValue} reams")
    print(f"Grid paper: {y.varValue} reams")
    print(f"Max profit: ${model.objVal:.2f}")
else:
    print("No optimal solution found.")
```

This code defines the 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 reams of each type of paper to produce and the maximum profit. Otherwise, it indicates that no optimal solution was found.