## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The restaurant needs to decide how many breakfast and lunch options to prepare to maximize profit, given the constraints on preparation and packaging time.

Let's define the decision variables:

* `B`: number of breakfast options to prepare
* `L`: number of lunch options to prepare

The objective function is to maximize profit:

* Profit per breakfast option: $10
* Profit per lunch option: $8
* Total profit: `10B + 8L`

The constraints are:

* Preparation time: 7 minutes per breakfast option, 8 minutes per lunch option, and 700 minutes available
* Packaging time: 2 minutes per breakfast option, 3 minutes per lunch option, and 500 minutes available

## Mathematical Formulation

The mathematical formulation of the problem is:

Maximize: `10B + 8L`

Subject to:

* `7B + 8L <= 700` (preparation time constraint)
* `2B + 3L <= 500` (packaging time constraint)
* `B >= 0` and `L >= 0` (non-negativity constraints)

## Gurobi Code

```python
import gurobi

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

    # Define the decision variables
    B = model.addVar(lb=0, name="Breakfast")
    L = model.addVar(lb=0, name="Lunch")

    # Define the objective function
    model.setObjective(10*B + 8*L, gurobi.GRB.MAXIMIZE)

    # Add the preparation time constraint
    model.addConstr(7*B + 8*L <= 700, name="Preparation_Time")

    # Add the packaging time constraint
    model.addConstr(2*B + 3*L <= 500, name="Packaging_Time")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of breakfast options: {B.varValue}")
        print(f"Number of lunch options: {L.varValue}")
        print(f"Maximum profit: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_restaurant_problem()
```