## Step 1: Define the variables and their attributes
We have four variables: 
- $x_0$: milligrams of calcium
- $x_1$: milligrams of zinc
- $x_2$: milligrams of vitamin B1
- $x_3$: milligrams of vitamin B5

Each variable has attributes defined by the resources $r_0$ and $r_1$, which represent the cognitive performance index and cardiovascular support index, respectively.

## Step 2: Formulate the objective function
The objective function to maximize is:
\[ 5.08x_0x_1 + 6.35x_1^2 + 6.26x_1x_2 + 6.59x_1x_3 + 3.56x_2^2 \]

## 3: Define the constraints
### Constraints from given indices
- $3.53x_0 \leq 376$
- $15.02x_0 \leq 184$
- $10.75x_1 \leq 376$
- $13.63x_1 \leq 184$
- $6.16x_2 \leq 376$
- $8.91x_2 \leq 184$
- $0.26x_3 \leq 376$
- $3.1x_3 \leq 184$

### Constraints on combined indices
- $6.16x_2 + 0.26x_3 \geq 81$
- $3.53^2x_0^2 + 10.75^2x_1^2 \geq 58$
- $15.02x_0 + 13.63x_1 + 3.1x_3 \geq 40$
- $15.02x_0 + 13.63x_1 + 8.91x_2 \geq 40$
- $13.63x_1 + 8.91x_2 + 3.1x_3 \geq 40$
- $15.02^2x_0^2 + 13.63^2x_1^2 + 3.1^2x_3^2 \geq 24$
- $15.02x_0 + 13.63x_1 + 8.91x_2 \geq 24$
- $13.63^2x_1^2 + 8.91^2x_2^2 + 3.1^2x_3^2 \geq 24$
- $15.02x_0 + 13.63x_1 + 3.1x_3 \geq 33$
- $15.02x_0 + 13.63x_1 + 8.91x_2 \geq 33$
- $13.63x_1 + 8.91x_2 + 3.1x_3 \geq 33$

### Constraints on squared and combined terms
- $3.53^2x_0^2 + 10.75^2x_1^2 \leq 186$
- $10.75x_1 + 0.26x_3 \leq 136$
- $3.53x_0 + 6.16x_2 \leq 190$
- $3.53^2x_0^2 + 6.16^2x_2^2 + 0.26^2x_3^2 \leq 370$
- $3.53x_0 + 10.75x_1 + 6.16x_2 + 0.26x_3 \leq 370$
- $15.02^2x_0^2 + 3.1^2x_3^2 \leq 159$
- $8.91x_2 + 3.1x_3 \leq 142$
- $15.02^2x_0^2 + 8.91^2x_2^2 \leq 50$
- $15.02^2x_0^2 + 13.63^2x_1^2 \leq 147$
- $15.02^2x_0^2 + 13.63^2x_1^2 + 3.1^2x_3^2 \leq 120$
- $15.02^2x_0^2 + 13.63^2x_1^2 + 8.91^2x_2^2 \leq 102$
- $15.02^2x_0^2 + 8.91^2x_2^2 + 3.1^2x_3^2 \leq 78$
- $15.02x_0 + 13.63x_1 + 8.91x_2 + 3.1x_3 \leq 78$

### Variable constraints
- $x_3$ must be an integer.

## 4: Implement the problem in Gurobi
```python
import gurobi

def optimize_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="calcium")
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="zinc")
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="vitamin_B1")
    x3 = model.addVar(lb=0, ub=gurobi.GRB.INFINITY, integrality=1, name="vitamin_B5")  # Integer constraint

    # Objective function
    model.setObjective(5.08*x0*x1 + 6.35*x1**2 + 6.26*x1*x2 + 6.59*x1*x3 + 3.56*x2**2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(3.53*x0 <= 376)
    model.addConstr(15.02*x0 <= 184)
    model.addConstr(10.75*x1 <= 376)
    model.addConstr(13.63*x1 <= 184)
    model.addConstr(6.16*x2 <= 376)
    model.addConstr(8.91*x2 <= 184)
    model.addConstr(0.26*x3 <= 376)
    model.addConstr(3.1*x3 <= 184)

    model.addConstr(6.16*x2 + 0.26*x3 >= 81)
    model.addConstr(3.53**2*x0**2 + 10.75**2*x1**2 >= 58)
    model.addConstr(15.02*x0 + 13.63*x1 + 3.1*x3 >= 40)
    model.addConstr(15.02*x0 + 13.63*x1 + 8.91*x2 >= 40)
    model.addConstr(13.63*x1 + 8.91*x2 + 3.1*x3 >= 40)
    model.addConstr(15.02**2*x0**2 + 13.63**2*x1**2 + 3.1**2*x3**2 >= 24)
    model.addConstr(15.02*x0 + 13.63*x1 + 8.91*x2 >= 24)
    model.addConstr(13.63**2*x1**2 + 8.91**2*x2**2 + 3.1**2*x3**2 >= 24)
    model.addConstr(15.02*x0 + 13.63*x1 + 3.1*x3 >= 33)
    model.addConstr(15.02*x0 + 13.63*x1 + 8.91*x2 >= 33)
    model.addConstr(13.63*x1 + 8.91*x2 + 3.1*x3 >= 33)

    model.addConstr(3.53**2*x0**2 + 10.75**2*x1**2 <= 186)
    model.addConstr(10.75*x1 + 0.26*x3 <= 136)
    model.addConstr(3.53*x0 + 6.16*x2 <= 190)
    model.addConstr(3.53**2*x0**2 + 6.16**2*x2**2 + 0.26**2*x3**2 <= 370)
    model.addConstr(3.53*x0 + 10.75*x1 + 6.16*x2 + 0.26*x3 <= 370)
    model.addConstr(15.02**2*x0**2 + 3.1**2*x3**2 <= 159)
    model.addConstr(8.91*x2 + 3.1*x3 <= 142)
    model.addConstr(15.02**2*x0**2 + 8.91**2*x2**2 <= 50)
    model.addConstr(15.02**2*x0**2 + 13.63**2*x1**2 <= 147)
    model.addConstr(15.02**2*x0**2 + 13.63**2*x1**2 + 3.1**2*x3**2 <= 120)
    model.addConstr(15.02**2*x0**2 + 13.63**2*x1**2 + 8.91**2*x2**2 <= 102)
    model.addConstr(15.02**2*x0**2 + 8.91**2*x2**2 + 3.1**2*x3**2 <= 78)
    model.addConstr(15.02*x0 + 13.63*x1 + 8.91*x2 + 3.1*x3 <= 78)

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Calcium: {x0.varValue}")
        print(f"Zinc: {x1.varValue}")
        print(f"Vitamin B1: {x2.varValue}")
        print(f"Vitamin B5: {x3.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```