To solve the given optimization problem using Gurobi, we first need to understand and possibly simplify the constraints provided. The objective function to be maximized is \(4x_0 + 9x_1\), where \(x_0\) represents the grams of carbohydrates and \(x_1\) represents the milligrams of magnesium.

Given constraints can be summarized as follows:
- Cardiovascular support index: \(7x_0 + 3x_1 \geq 36\) and \(7x_0 + 3x_1 \leq 103\).
- Immune support index: \(10x_0 + x_1 \geq 40\) and \(10x_0 + x_1 \leq 78\).
- Energy stability index: \(3x_0 + 13x_1 \geq 70\) and \(3x_0 + 13x_1 \leq 143\).
- Additional constraint: \(-10x_0 + 5x_1 \geq 0\).

The constraints provided seem to have some redundancy, particularly with the upper bounds for each index. For instance, having both "at least" and "at most" conditions that are essentially the same can be simplified.

Let's write the Gurobi code in Python to solve this optimization problem:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="grams_of_carbohydrates")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_magnesium")

# Objective function: Maximize 4*x0 + 9*x1
m.setObjective(4*x0 + 9*x1, GRB.MAXIMIZE)

# Constraints
m.addConstr(7*x0 + 3*x1 >= 36, "cardiovascular_support_index_min")
m.addConstr(7*x0 + 3*x1 <= 103, "cardiovascular_support_index_max")

m.addConstr(10*x0 + x1 >= 40, "immune_support_index_min")
m.addConstr(10*x0 + x1 <= 78, "immune_support_index_max")

m.addConstr(3*x0 + 13*x1 >= 70, "energy_stability_index_min")
m.addConstr(3*x0 + 13*x1 <= 143, "energy_stability_index_max")

m.addConstr(-10*x0 + 5*x1 >= 0, "additional_constraint")

# Solve the model
m.optimize()

if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Grams of carbohydrates: {x0.x}")
    print(f"Milligrams of magnesium: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```