## Problem Description and Formulation

The problem is an optimization problem where we need to maximize the objective function:

\[ 9 \times \text{milligrams of calcium} + 2 \times \text{grams of protein} + 8 \times \text{milligrams of vitamin B9} \]

subject to several constraints related to the kidney support index from each variable and their combinations.

## Constraints

1. The kidney support index for milligrams of calcium is 7.69.
2. Grams of protein have a kidney support index of 6.48.
3. Milligrams of vitamin B9 each have a kidney support index of 3.53.
4. The total combined kidney support index from grams of protein plus milligrams of vitamin B9 should be no less than 47.
5. The total combined kidney support index from milligrams of calcium, grams of protein, and milligrams of vitamin B9 has to be at minimum 64.
6. The total combined kidney support index from grams of protein and milligrams of vitamin B9 must be 157 or less.
7. The total combined kidney support index from milligrams of calcium and milligrams of vitamin B9 has to be 158 at a maximum.
8. The total combined kidney support index from milligrams of calcium plus grams of protein should be equal to or less than 192.
9. The total combined kidney support index from milligrams of calcium, grams of protein, and milligrams of vitamin B9 should be at most 192.

## Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    calcium_mg = model.addVar(name="calcium_mg", lb=0)  # Non-negative, can be non-integer
    protein_g = model.addVar(name="protein_g", lb=0)  # Non-negative, can be non-integer
    vitamin_B9_mg = model.addVar(name="vitamin_B9_mg", lb=0)  # Non-negative, can be non-integer

    # Define coefficients
    calcium_kidney_index = 7.69
    protein_kidney_index = 6.48
    vitamin_B9_kidney_index = 3.53

    # Objective function
    model.setObjective(9 * calcium_mg + 2 * protein_g + 8 * vitamin_B9_mg, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstraint(protein_kidney_index * protein_g + vitamin_B9_kidney_index * vitamin_B9_mg >= 47)
    model.addConstraint(calcium_kidney_index * calcium_mg + protein_kidney_index * protein_g + vitamin_B9_kidney_index * vitamin_B9_mg >= 64)
    model.addConstraint(protein_kidney_index * protein_g + vitamin_B9_kidney_index * vitamin_B9_mg <= 157)
    model.addConstraint(calcium_kidney_index * calcium_mg + vitamin_B9_kidney_index * vitamin_B9_mg <= 158)
    model.addConstraint(calcium_kidney_index * calcium_mg + protein_kidney_index * protein_g <= 192)
    model.addConstraint(calcium_kidney_index * calcium_mg + protein_kidney_index * protein_g + vitamin_B9_kidney_index * vitamin_B9_mg <= 192)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Milligrams of Calcium: {calcium_mg.varValue}")
        print(f"Grams of Protein: {protein_g.varValue}")
        print(f"Milligrams of Vitamin B9: {vitamin_B9_mg.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_kidney_support()
```