## Problem Description and Formulation

The problem is a linear programming optimization problem where we need to minimize the cost of buying two types of instant coffees, Vanilla and Mocha, while meeting the requirements for caffeine and sugar intake.

Let's define the decision variables:
- \(V\): The number of packages of Vanilla flavor coffee to buy.
- \(M\): The number of packages of Mocha flavor coffee to buy.

The objective is to minimize the total cost, given by \(2V + 3M\), since a package of Vanilla flavor costs $2 and a package of Mocha flavor costs $3.

The constraints are:
1. Caffeine requirement: \(2V + 3M \geq 60\) (at least 60 units of caffeine).
2. Sugar requirement: \(2V + 5M \geq 50\) (at least 50 units of sugar).
3. Non-negativity: \(V \geq 0, M \geq 0\) (we cannot buy a negative number of packages).

## Gurobi Code

To solve this problem using Gurobi in Python, we will use the Gurobi Python API. First, ensure you have Gurobi installed in your Python environment. You can install it via pip if you have the Gurobi license and credentials set up:

```bash
pip install gurobi
```

Here's the Gurobi code for the problem:

```python
import gurobi as gp

# Create a new model
model = gp.Model("coffee_problem")

# Define the decision variables
V = model.addVar(lb=0, name="Vanilla")
M = model.addVar(lb=0, name="Mocha")

# Objective: minimize cost
model.setObjective(2*V + 3*M, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(2*V + 3*M >= 60, name="caffeine_requirement")
model.addConstr(2*V + 5*M >= 50, name="sugar_requirement")

# Optimize the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal cost: ${model.objVal:.2f}")
    print(f"Buy {V.varValue:.0f} packages of Vanilla flavor coffee.")
    print(f"Buy {M.varValue:.0f} packages of Mocha flavor coffee.")
else:
    print("The problem is infeasible or no solution exists.")
```