## Problem Description and Formulation

The problem is an optimization problem where we need to maximize an objective function subject to several constraints. The objective function to maximize is:

\[ 2 \times \text{milligrams of vitamin B4} + 5 \times \text{milligrams of potassium} + 8 \times \text{milligrams of vitamin B1} + 9 \times \text{milligrams of vitamin B6} \]

The variables are:
- \(x_0\): milligrams of vitamin B4
- \(x_1\): milligrams of potassium
- \(x_2\): milligrams of vitamin B1
- \(x_3\): milligrams of vitamin B6

The constraints are given based on two indices: immune support index and cardiovascular support index.

## Constraints

1. Individual indices for each variable:
   - \(x_0\): Immune = 6.49, Cardiovascular = 2.09
   - \(x_1\): Immune = 15.8, Cardiovascular = 0.7
   - \(x_2\): Immune = 13.81, Cardiovascular = 4.16
   - \(x_3\): Immune = 7.23, Cardiovascular = 9.55

2. Combined constraints:
   - \(6.49x_0 + 7.23x_3 \geq 49\)
   - \(2.09x_0 + 9.55x_3 \geq 34\)
   - \(15.8x_1 + 13.81x_2 \leq 259\)
   - \(15.8x_1 + 13.81x_2 + 7.23x_3 \leq 142\)
   - \(6.49x_0 + 15.8x_1 + 13.81x_2 \leq 156\)
   - \(6.49x_0 + 15.8x_1 + 13.81x_2 + 7.23x_3 \leq 148\)
   - \(4.16x_2 + 9.55x_3 \leq 295\)
   - \(0.7x_1 + 4.16x_2 \leq 178\)
   - \(0.7x_1 + 4.16x_2 + 9.55x_3 \leq 113\)
   - \(2.09x_0 + 0.7x_1 + 4.16x_2 \leq 96\)
   - \(2.09x_0 + 0.7x_1 + 4.16x_2 + 9.55x_3 \leq 96\)

## Gurobi Code

```python
import gurobipy as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define variables
x0 = m.addVar(name="milligrams_of_vitamin_B4", lb=0)
x1 = m.addVar(name="milligrams_of_potassium", lb=0)
x2 = m.addVar(name="milligrams_of_vitamin_B1", lb=0)
x3 = m.addVar(name="milligrams_of_vitamin_B6", lb=0)

# Objective function
m.setObjective(2*x0 + 5*x1 + 8*x2 + 9*x3, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(6.49*x0 + 7.23*x3 >= 49)
m.addConstr(2.09*x0 + 9.55*x3 >= 34)
m.addConstr(15.8*x1 + 13.81*x2 <= 259)
m.addConstr(15.8*x1 + 13.81*x2 + 7.23*x3 <= 142)
m.addConstr(6.49*x0 + 15.8*x1 + 13.81*x2 <= 156)
m.addConstr(6.49*x0 + 15.8*x1 + 13.81*x2 + 7.23*x3 <= 148)
m.addConstr(4.16*x2 + 9.55*x3 <= 295)
m.addConstr(0.7*x1 + 4.16*x2 <= 178)
m.addConstr(0.7*x1 + 4.16*x2 + 9.55*x3 <= 113)
m.addConstr(2.09*x0 + 0.7*x1 + 4.16*x2 <= 96)
m.addConstr(2.09*x0 + 0.7*x1 + 4.16*x2 + 9.55*x3 <= 96)

# Optimize
m.optimize()

# Print solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Milligrams of vitamin B4: ", x0.varValue)
    print("Milligrams of potassium: ", x1.varValue)
    print("Milligrams of vitamin B1: ", x2.varValue)
    print("Milligrams of vitamin B6: ", x3.varValue)
else:
    print("The problem is infeasible")
```