## Problem Description and Formulation

The problem is an optimization problem with the goal to maximize an objective function subject to several constraints. The variables are:
- Milligrams of vitamin B9 (`B9`)
- Milligrams of vitamin B4 (`B4`)
- Grams of fiber (`fiber`)
- Milligrams of vitamin K (`K`)

The objective function to maximize is:
\[ 7 \times B9 + 8 \times B4 + 7 \times fiber + 5 \times K \]

Subject to the following constraints:
1. Kidney support index for `B9` is 11.
2. Kidney support index for `B4` is 9.
3. Kidney support index for `fiber` is 11.
4. Kidney support index for `K` is 3.
5. \(-8 \times B4 + fiber \geq 0\)
6. \(9 \times B4 + 3 \times K \leq 64\)
7. \(11 \times B9 + 9 \times B4 \leq 75\)
8. \(11 \times B9 + 11 \times fiber \leq 49\)
9. \(11 \times fiber + 3 \times K \leq 45\)
10. \(11 \times B9 + 3 \times K \leq 30\)
11. \(11 \times B9 + 9 \times B4 + 11 \times fiber + 3 \times K \leq 30\)

## Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    B9 = model.addVar(name="B9", lb=0)  # Milligrams of vitamin B9
    B4 = model.addVar(name="B4", lb=0)  # Milligrams of vitamin B4
    fiber = model.addVar(name="fiber", lb=0)  # Grams of fiber
    K = model.addVar(name="K", lb=0)  # Milligrams of vitamin K

    # Objective function
    model.setObjective(7 * B9 + 8 * B4 + 7 * fiber + 5 * K, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstraint(B9 <= 11, name="B9_kidney_support")
    model.addConstraint(B4 <= 9, name="B4_kidney_support")
    model.addConstraint(fiber <= 11, name="fiber_kidney_support")
    model.addConstraint(K <= 3, name="K_kidney_support")

    model.addConstraint(-8 * B4 + fiber >= 0, name="B4_fiber_constraint")
    model.addConstraint(9 * B4 + 3 * K <= 64, name="B4_K_constraint")
    model.addConstraint(11 * B9 + 9 * B4 <= 75, name="B9_B4_constraint")
    model.addConstraint(11 * B9 + 11 * fiber <= 49, name="B9_fiber_constraint")
    model.addConstraint(11 * fiber + 3 * K <= 45, name="fiber_K_constraint")
    model.addConstraint(11 * B9 + 3 * K <= 30, name="B9_K_constraint")
    model.addConstraint(11 * B9 + 9 * B4 + 11 * fiber + 3 * K <= 30, name="all_variables_constraint")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of vitamin B9: {B9.varValue}")
        print(f"Milligrams of vitamin B4: {B4.varValue}")
        print(f"Grams of fiber: {fiber.varValue}")
        print(f"Milligrams of vitamin K: {K.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_kidney_support()
```