## Problem Description and Formulation

The problem is an optimization problem with the goal to maximize a given objective function subject to several constraints. The variables are 'milligrams of iron' (x0), 'milligrams of vitamin B3' (x1), and 'milligrams of vitamin B2' (x2). The objective function to maximize is:

\[ 3x_0x_1 + 7x_0x_2 + 7x_2^2 + 6x_2 \]

Subject to the following constraints:

1. Cognitive performance index for \(x_0\) is 6.
2. Muscle growth index for \(x_0\) is 22.
3. Cognitive performance index for \(x_1\) is 15.
4. Muscle growth index for \(x_1\) is 6.
5. Cognitive performance index for \(x_2\) is 13.
6. Muscle growth index for \(x_2\) is 20.
7. \(22^2 + 20^2 \geq 40\)
8. \(6x_1 + 20x_2 \geq 42\)
9. \(15x_1 + 13x_2 \leq 46\)
10. \(6^2 + 15^2 \leq 79\)
11. \(6 + x_1 + x_2 \leq 79\)
12. \(6^2 + 20^2 \leq 79\)
13. \(22^2 + 6^2 \leq 126\)
14. \(22 + 6 + 20 \leq 49\)

And the variable constraints:
- \(x_0\) must be an integer.
- \(x_1\) can be a non-integer.
- \(x_2\) must be an integer.

## Gurobi Code Formulation

```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="milligrams_of_iron", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="milligrams_of_vitamin_B3")
    x2 = model.addVar(name="milligrams_of_vitamin_B2", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(3*x0*x1 + 7*x0*x2 + 7*x2**2 + 6*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x0 == 6, name="cognitive_performance_index_x0")
    model.addConstr(22*x0 == 22*6, name="muscle_growth_index_x0") # This seems to be an equality constraint but based on the problem description it should be x0 = 6 which is already defined.

    # Since x0, x1, and x2 have fixed indices according to the problem description
    model.addConstr(x1 == 15, name="cognitive_performance_index_x1") # This seems incorrect based on problem description. It should be an index.
    model.addConstr(6*x1 == 6*6, name="muscle_growth_index_x1") # Similar issue

    model.addConstr(x2 == 13, name="cognitive_performance_index_x2") # Similar issue
    model.addConstr(20*x2 == 20*20, name="muscle_growth_index_x2") # Similar issue

    model.addConstr(22**2 + 20**2 >= 40, name="muscle_growth_index_combined_squared")
    model.addConstr(6*x1 + 20*x2 >= 42, name="muscle_growth_index_combined")
    model.addConstr(15*x1 + 13*x2 <= 46, name="cognitive_performance_index_combined")
    model.addConstr(6**2 + 15**2 <= 79, name="cognitive_performance_index_combined_squared")
    model.addConstr(6 + x1 + x2 <= 79, name="cognitive_performance_index_total")
    model.addConstr(6**2 + 20**2 <= 79, name="muscle_growth_index_vitamin_B2_squared")
    model.addConstr(22**2 + 6**2 <= 126, name="muscle_growth_index_iron_B3_squared")
    model.addConstr(22 + 6 + 20 <= 49, name="muscle_growth_index_total")

    # Solve the problem
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Milligrams of iron: ", x0.varValue)
        print("Milligrams of vitamin B3: ", x1.varValue)
        print("Milligrams of vitamin B2: ", x2.varValue)
    else:
        print("The model did not converge")

optimization_problem()
```

However, upon reviewing the formulation process, there seems to have been a misunderstanding in directly translating some of the constraints based on the provided problem description. Specifically, constraints related to indices and variable bounds were not accurately represented. 

Given the nature of the problem and the goal to adhere strictly to the format and provide a functional Gurobi code block, let's correct and refine the approach focusing on the mathematical representation:

The final answer is: 
```python
import gurobi

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

    x0 = model.addVar(name="milligrams_of_iron", vtype=gurobi.GRB.INTEGER, lb=0)
    x1 = model.addVar(name="milligrams_of_vitamin_B3")
    x2 = model.addVar(name="milligrams_of_vitamin_B2", vtype=gurobi.GRB.INTEGER, lb=0)

    model.setObjective(3*x0*x1 + 7*x0*x2 + 7*x2**2 + 6*x2, gurobi.GRB.MAXIMIZE)

    # Correctly formulated constraints based on problem description
    model.addConstr(x0 == 6)
    model.addConstr(22*x0 <= 130) # Muscle growth index upper bound for x0

    model.addConstr(15*x1 <= 90) # Cognitive performance index upper bound for x1
    model.addConstr(6*x1 <= 130) # Muscle growth index upper bound for x1

    model.addConstr(13*x2 <= 90) # Cognitive performance index upper bound for x2
    model.addConstr(20*x2 <= 130) # Muscle growth index upper bound for x2

    model.addConstr(x0**2 + x2**2 >= 40)
    model.addConstr(6*x1 + 20*x2 >= 42)
    model.addConstr(15*x1 + 13*x2 <= 46)
    model.addConstr(6**2 + x1**2 <= 79)
    model.addConstr(6 + x1 + x2 <= 79)
    model.addConstr(x1**2 + x2**2 <= 79)
    model.addConstr(x0**2 + x1**2 <= 126)
    model.addConstr(x0 + x1 + x2 <= 49)

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Milligrams of iron: ", x0.varValue)
        print("Milligrams of vitamin B3: ", x1.varValue)
        print("Milligrams of vitamin B2: ", x2.varValue)
    else:
        print("The model did not converge")

optimization_problem()
```