## Problem Description and Formulation

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

\[ 8.82 \times \text{milligrams of zinc} + 1.66 \times \text{milligrams of vitamin B6} \]

subject to several constraints.

### Constraints

1. **Individual Index Constraints:**
   - Kidney support index for milligrams of zinc: 26
   - Cardiovascular support index for milligrams of zinc: 7
   - Cognitive performance index for milligrams of zinc: 28
   - Kidney support index for milligrams of vitamin B6: 29
   - Cardiovascular support index for milligrams of vitamin B6: 4
   - Cognitive performance index for milligrams of vitamin B6: 7

2. **Combined Index Constraints:**
   - Total kidney support index \(\geq 85\)
   - Total cardiovascular support index \(\geq 60\)
   - Total cognitive performance index \(\geq 24\)
   - \(-6 \times \text{milligrams of zinc} + 4 \times \text{milligrams of vitamin B6} \geq 0\)
   - Total kidney support index \(\leq 158\)
   - Total cardiovascular support index \(\leq 119\)
   - Total cognitive performance index \(\leq 89\)

### Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    zinc = model.addVar(lb=0, name="milligrams_of_zinc", vtype=gurobi.GRB.CONTINUOUS)
    vitamin_b6 = model.addVar(lb=0, name="milligrams_of_vitamin_B6", vtype=gurobi.GRB.CONTINUOUS)

    # Objective function
    model.setObjective(8.82 * zinc + 1.66 * vitamin_b6, gurobi.GRB.MAXIMIZE)

    # Constraints
    # Individual Index Constraints (not directly constraints but used in combined constraints)
    kidney_support_zinc = 26
    cardiovascular_support_zinc = 7
    cognitive_performance_zinc = 28
    kidney_support_b6 = 29
    cardiovascular_support_b6 = 4
    cognitive_performance_b6 = 7

    # Combined Index Constraints
    model.addConstr(kidney_support_zinc * zinc + kidney_support_b6 * vitamin_b6 >= 85, name="kidney_support_min")
    model.addConstr(cardiovascular_support_zinc * zinc + cardiovascular_support_b6 * vitamin_b6 >= 60, name="cardiovascular_support_min")
    model.addConstr(cognitive_performance_zinc * zinc + cognitive_performance_b6 * vitamin_b6 >= 24, name="cognitive_performance_min")
    model.addConstr(-6 * zinc + 4 * vitamin_b6 >= 0, name="linear_constraint")
    model.addConstr(kidney_support_zinc * zinc + kidney_support_b6 * vitamin_b6 <= 158, name="kidney_support_max")
    model.addConstr(cardiovascular_support_zinc * zinc + cardiovascular_support_b6 * vitamin_b6 <= 119, name="cardiovascular_support_max")
    model.addConstr(cognitive_performance_zinc * zinc + cognitive_performance_b6 * vitamin_b6 <= 89, name="cognitive_performance_max")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Milligrams of Zinc: {zinc.varValue}")
        print(f"Milligrams of Vitamin B6: {vitamin_b6.varValue}")
        print(f"Objective Function Value: {model.objVal}")
    else:
        print("The model is infeasible.")

solve_optimization_problem()
```