## Problem Description and Formulation

The problem described is a linear programming optimization problem. The goal is to maximize profit by determining the number of bottles of Alpha and Beta drugs to produce, given certain constraints.

### Variables
- \(x\): Number of bottles of Alpha to produce
- \(y\): Number of bottles of Beta to produce

### Objective Function
The profit from one bottle of Alpha is $4, and from one bottle of Beta is $6. Therefore, the total profit \(P\) can be represented as:
\[P = 4x + 6y\]

### Constraints
1. **Extract Limitation**: 2000 grams of extract are available. Given that one bottle of Alpha requires 15 grams and one bottle of Beta requires 25 grams, we have:
\[15x + 25y \leq 2000\]

2. **Demand Constraint**: At least three times as many Alpha bottles are needed than Beta bottles:
\[x \geq 3y\]

3. **Minimum Beta Production**: A minimum of 10 bottles of Beta need to be made:
\[y \geq 10\]

4. **Non-Negativity**: The number of bottles cannot be negative:
\[x \geq 0, y \geq 0\]

## Gurobi Code

```python
import gurobi

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

    # Define variables
    x = model.addVar(name="Alpha", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    y = model.addVar(name="Beta", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: Maximize profit
    model.setObjective(4 * x + 6 * y, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(15 * x + 25 * y <= 2000, name="extract_limitation")
    model.addConstr(x >= 3 * y, name="demand_constraint")
    model.addConstr(y >= 10, name="min_beta_production")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: Alpha = {x.varValue}, Beta = {y.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found")

solve_optimization_problem()
```

This code defines the optimization problem using Gurobi's Python interface, sets up the objective function and constraints according to the problem description, and solves the linear programming problem to find the optimal production levels of Alpha and Beta that maximize profit.