To solve the given optimization problem using Gurobi, we need to first understand the objective function and the constraints. The objective is to maximize `5.14 * grams_of_fat + 5.3 * milligrams_of_vitamin_B12`. The constraints are based on the cognitive performance index and cardiovascular support index for both grams of fat and milligrams of vitamin B12, as well as their combined effects.

Given:
- Objective function: Maximize `5.14 * grams_of_fat + 5.3 * milligrams_of_vitamin_B12`
- Constraints:
  - Cognitive performance index for grams of fat: 17
  - Cardiovascular support index for grams of fat: 7
  - Cognitive performance index for milligrams of vitamin B12: 17
  - Cardiovascular support index for milligrams of vitamin B12: 17
  - Minimum combined cognitive performance index: 16
  - Minimum combined cardiovascular support index: 48
  - Constraint: `-4 * grams_of_fat + 10 * milligrams_of_vitamin_B12 >= 0`
  - Maximum combined cognitive performance index: 38
  - Maximum combined cardiovascular support index: 104

The constraints related to the indices of grams of fat and milligrams of vitamin B12 seem to be more about their individual properties rather than constraints on the variables in the optimization problem. However, the combined effects and the specific linear constraint involving both variables are what will guide our formulation.

Let's define the decision variables:
- `grams_of_fat`: The amount of grams of fat.
- `milligrams_of_vitamin_B12`: The amount of milligrams of vitamin B12.

Now, translating this into Gurobi code:

```python
from gurobipy import *

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

# Define the decision variables
grams_of_fat = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="grams_of_fat")
milligrams_of_vitamin_B12 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B12")

# Define the objective function
m.setObjective(5.14 * grams_of_fat + 5.3 * milligrams_of_vitamin_B12, GRB.MAXIMIZE)

# Add constraints
m.addConstr(17 * grams_of_fat + 17 * milligrams_of_vitamin_B12 >= 16, name="min_cognitive_performance")
m.addConstr(7 * grams_of_fat + 17 * milligrams_of_vitamin_B12 >= 48, name="min_cardiovascular_support")
m.addConstr(-4 * grams_of_fat + 10 * milligrams_of_vitamin_B12 >= 0, name="linear_constraint")
m.addConstr(17 * grams_of_fat + 17 * milligrams_of_vitamin_B12 <= 38, name="max_cognitive_performance")
m.addConstr(7 * grams_of_fat + 17 * milligrams_of_vitamin_B12 <= 104, name="max_cardiovascular_support")

# Optimize the model
m.optimize()

# Print the results
for v in m.getVars():
    print(f"{v.varName}: {v.x}")
print(f"Objective: {m.objVal}")
```

This code sets up a Gurobi model with the given objective function and constraints, then solves it to find the optimal values of `grams_of_fat` and `milligrams_of_vitamin_B12`. Note that this formulation assumes all constraints are linear and that the variables can be continuous, as indicated by the problem statement.