## Problem Description and Formulation

The problem is a linear programming optimization problem. We need to minimize the cost of obtaining vitamin A and vitamin B from two supplement drinks: carrot juice and lemon juice. The goal is to find the optimal mix of these drinks that meets the daily recommended intake of 25 units of each vitamin while minimizing the total cost.

## Decision Variables

Let \(x\) be the number of servings of carrot juice and \(y\) be the number of servings of lemon juice.

## Objective Function

The objective is to minimize the total cost, which is given by \(3.5x + 6y\).

## Constraints

1. Vitamin A constraint: \(8x + 3y \geq 25\)
2. Vitamin B constraint: \(3x + 6y \geq 25\)
3. Non-negativity constraints: \(x \geq 0, y \geq 0\)

## Gurobi Code

```python
import gurobi

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

    # Define the decision variables
    x = model.addVar(lb=0, name="carrot_juice_servings", vtype=gurobi.GRB.CONTINUOUS)
    y = model.addVar(lb=0, name="lemon_juice_servings", vtype=gurobi.GRB.CONTINUOUS)

    # Define the objective function
    model.setObjective(3.5 * x + 6 * y, gurobi.GRB.MINIMIZE)

    # Add the constraints
    model.addConstr(8 * x + 3 * y >= 25, name="vitamin_A_constraint")
    model.addConstr(3 * x + 6 * y >= 25, name="vitamin_B_constraint")

    # Optimize the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print(f"Optimal solution found. Carrot juice servings: {x.varValue}, Lemon juice servings: {y.varValue}")
        print(f"Minimum cost: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

# Run the optimization problem
solve_optimization_problem()
```