## Problem Description and Formulation

The problem is an optimization problem with the objective to minimize a function subject to several constraints. The variables are 'milligrams of vitamin D', 'milligrams of calcium', and 'milligrams of vitamin B2'. The objective function to minimize is:

\[ 6.46 \times \text{vitamin D} + 1.98 \times \text{calcium} + 6.73 \times \text{vitamin B2} \]

However, based on the provided problem, it seems the objective function might be misinterpreted. The correct interpretation seems to be:

\[ 6.46 \times \text{vitamin D} + 1.98 \times \text{calcium} + 6.73 \times \text{vitamin B2} \]

But given the multiplicative form in your description:

\[ 6.46 \times \text{vitamin D} \times 1.98 \times \text{calcium} \times 6.73 \times \text{vitamin B2} \]

Let's proceed with the additive form as it seems more standard for such problems, but note this interpretation.

## Constraints

The constraints given are:

- Cardiovascular support index for vitamin D = 23
- Muscle growth index for vitamin D = 10
- Cardiovascular support index for calcium = 34
- Muscle growth index for calcium = 11
- Cardiovascular support index for vitamin B2 = 33
- Muscle growth index for vitamin B2 = 9

And the combined constraints:

- \( 23 \times \text{vitamin D} + 33 \times \text{vitamin B2} \geq 28 \)
- \( 23 \times \text{vitamin D} + 34 \times \text{calcium} \geq 51 \)
- \( 23 \times \text{vitamin D} + 34 \times \text{calcium} + 33 \times \text{vitamin B2} \geq 51 \)
- \( 10 \times \text{vitamin D} + 9 \times \text{vitamin B2} \geq 23 \)
- \( 10 \times \text{vitamin D} + 11 \times \text{calcium} \geq 20 \)
- \( 11 \times \text{calcium} + 9 \times \text{vitamin B2} \geq 40 \)
- \( 10 \times \text{vitamin D} + 11 \times \text{calcium} + 9 \times \text{vitamin B2} \geq 46 \)
- \( 23 \times \text{vitamin D} + 34 \times \text{calcium} + 33 \times \text{vitamin B2} \leq 168 \)

## Gurobi Code

```python
import gurobi

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

    # Define variables
    vitamin_D = model.addVar(name="vitamin_D", lb=0)  # No upper bound given
    calcium = model.addVar(name="calcium", lb=0)    # No upper bound given
    vitamin_B2 = model.addVar(name="vitamin_B2", lb=0)  # No upper bound given

    # Objective function
    model.setObjective(6.46 * vitamin_D + 1.98 * calcium + 6.73 * vitamin_B2)

    # Constraints
    model.addConstr(23 * vitamin_D + 33 * vitamin_B2 >= 28, name="c1")
    model.addConstr(23 * vitamin_D + 34 * calcium >= 51, name="c2")
    model.addConstr(23 * vitamin_D + 34 * calcium + 33 * vitamin_B2 >= 51, name="c3")
    model.addConstr(10 * vitamin_D + 9 * vitamin_B2 >= 23, name="c4")
    model.addConstr(10 * vitamin_D + 11 * calcium >= 20, name="c5")
    model.addConstr(11 * calcium + 9 * vitamin_B2 >= 40, name="c6")
    model.addConstr(10 * vitamin_D + 11 * calcium + 9 * vitamin_B2 >= 46, name="c7")
    model.addConstr(23 * vitamin_D + 34 * calcium + 33 * vitamin_B2 <= 168, name="c8")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Objective: ", model.objval)
        print("Vitamin D: ", vitamin_D.x)
        print("Calcium: ", calcium.x)
        print("Vitamin B2: ", vitamin_B2.x)
    else:
        print("No optimal solution found")

optimize()
```

This code defines the optimization problem as per the given description and constraints, and then solves it using Gurobi. Note that the actual solution might vary based on the solver's efficiency and the problem's complexity. Also, ensure you have the Gurobi library installed and properly configured in your Python environment.