## Step 1: Define the symbolic representation of the problem

Let's define the symbolic variables:
- $x_1$ = cups of orange juice
- $x_2$ = cups of apple juice

The objective is to minimize the amount of Vitamin K. The amount of Vitamin K in $x_1$ cups of orange juice and $x_2$ cups of apple juice is $3x_1 + 9x_2$.

## Step 2: Formulate the objective function and constraints

The objective function to minimize is: $3x_1 + 9x_2$

The constraints based on the vitamin requirements are:
- Vitamin A: $6x_1 + 10x_2 \geq 100$
- Vitamin D: $5x_1 + 3x_2 \geq 200$
- Vitamin E: $12x_1 + 15x_2 \leq 150$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## 3: Convert the problem into a Gurobi-compatible format

```json
{
'sym_variables': [('x1', 'cups of orange juice'), ('x2', 'cups of apple juice')],
'objective_function': '3*x1 + 9*x2',
'constraints': [
    '6*x1 + 10*x2 >= 100',
    '5*x1 + 3*x2 >= 200',
    '12*x1 + 15*x2 <= 150',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 4: Implement the problem in Gurobi Python

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="orange_juice", lb=0)
    x2 = model.addVar(name="apple_juice", lb=0)

    # Define the objective function
    model.setObjective(3*x1 + 9*x2, gurobi.MINIMIZE)

    # Define the constraints
    model.addConstr(6*x1 + 10*x2 >= 100, name="vitamin_A")
    model.addConstr(5*x1 + 3*x2 >= 200, name="vitamin_D")
    model.addConstr(12*x1 + 15*x2 <= 150, name="vitamin_E")

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.OPTIMAL:
        print("Optimal solution found.")
        print(f"Cups of orange juice: {x1.varValue}")
        print(f"Cups of apple juice: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_vitamin_mix_problem()
```