## Problem Description and Formulation

The problem is an optimization problem with a quadratic objective function and linear constraints. The goal is to maximize the objective function subject to various constraints on the cardiovascular and digestive support indices.

## Variables and Resources

The variables are:
- $x_0$: milligrams of vitamin D
- $x_1$: milligrams of vitamin B4
- $x_2$: milligrams of vitamin B12

The resources/attributes are:
- $r_0$: cardiovascular support index
- $r_1$: digestive support index

## Objective Function

The objective function to maximize is:
\[ 4x_0^2 + 7x_0x_1 + 5x_1x_2 + 9x_0 + 6x_2 \]

## Constraints

The constraints are:
- $8x_0 + 6x_1 \geq 4$
- $8x_0 + 6x_1 + 4x_2 \geq 5$
- $8x_0 + 4x_2 \leq 27$
- $8x_0 + 6x_1 \leq 17$
- $6x_1 + 4x_2 \leq 21$
- $8x_0 + 6x_1 + 4x_2 \leq 21$
- $3x_0 + 2x_1 \leq 15$
- $3x_0 + 7x_2 \leq 22$
- $3x_0 + 2x_1 + 7x_2 \leq 22$
- $x_0$ can be fractional
- $x_1$ is an integer
- $x_2$ is an integer

## Gurobi Code

```python
import gurobi

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

    # Define variables
    x0 = model.addVar(lb=-float('inf'), ub=float('inf'), name="milligrams of vitamin D")
    x1 = model.addVar(lb=-float('inf'), ub=float('inf'), vtype=gurobi.GRB.INTEGER, name="milligrams of vitamin B4")
    x2 = model.addVar(lb=-float('inf'), ub=float('inf'), vtype=gurobi.GRB.INTEGER, name="milligrams of vitamin B12")

    # Objective function
    model.setObjective(4*x0**2 + 7*x0*x1 + 5*x1*x2 + 9*x0 + 6*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(8*x0 + 6*x1 >= 4, name="cardiovascular support index 1")
    model.addConstr(8*x0 + 6*x1 + 4*x2 >= 5, name="cardiovascular support index 2")
    model.addConstr(8*x0 + 4*x2 <= 27, name="cardiovascular support index 3")
    model.addConstr(8*x0 + 6*x1 <= 17, name="cardiovascular support index 4")
    model.addConstr(6*x1 + 4*x2 <= 21, name="cardiovascular support index 5")
    model.addConstr(8*x0 + 6*x1 + 4*x2 <= 21, name="cardiovascular support index 6")
    model.addConstr(3*x0 + 2*x1 <= 15, name="digestive support index 1")
    model.addConstr(3*x0 + 7*x2 <= 22, name="digestive support index 2")
    model.addConstr(3*x0 + 2*x1 + 7*x2 <= 22, name="digestive support index 3")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Milligrams of vitamin D: ", x0.varValue)
        print("Milligrams of vitamin B4: ", x1.varValue)
        print("Milligrams of vitamin B12: ", x2.varValue)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```