## Problem Description and Formulation

The problem is an optimization problem with two variables: 'grams of fat' and 'milligrams of vitamin C'. The objective is to minimize the function 8 times the amount of grams of fat plus 4 multiplied by the number of milligrams of vitamin C, subject to several constraints.

## Constraints

1. The digestive support index for grams of fat is 14.
2. The cognitive performance index of grams of fat is 7.
3. Milligrams of vitamin C have a digestive support index of 12.
4. The cognitive performance index of milligrams of vitamin C is 15.
5. The total combined digestive support index from grams of fat and milligrams of vitamin C should be greater than or equal to 21.
6. The total combined cognitive performance index from grams of fat and milligrams of vitamin C must be 38 or more.
7. Minus one times the number of grams of fat, plus 6 times the number of milligrams of vitamin C must be greater than or equal to zero.
8. The total combined digestive support index from grams of fat and milligrams of vitamin C must be at maximum 71.
9. The total combined cognitive performance index from grams of fat and milligrams of vitamin C has to be 88 at maximum.

## Gurobi Code

```python
import gurobi

# Create a new Gurobi model
m = gurobi.Model()

# Define variables
fat = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="fat")
vitamin_c = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="vitamin_c")

# Objective function: Minimize 8 * fat + 4 * vitamin_c
m.setObjective(8 * fat + 4 * vitamin_c, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(14 * fat + 12 * vitamin_c >= 21, name="digestive_support_index_min")
m.addConstr(7 * fat + 15 * vitamin_c >= 38, name="cognitive_performance_index_min")
m.addConstr(-fat + 6 * vitamin_c >= 0, name="fat_vitamin_c_relation")
m.addConstr(14 * fat + 12 * vitamin_c <= 71, name="digestive_support_index_max")
m.addConstr(7 * fat + 15 * vitamin_c <= 88, name="cognitive_performance_index_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Fat: {fat.varValue}")
    print(f"Vitamin C: {vitamin_c.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("No optimal solution found.")
```

## Note

The above code assumes that the variables 'grams of fat' and 'milligrams of vitamin C' can take any real value. If they must be integers, you can add `vtype='I'` when creating the variables. However, based on your problem description, it seems that non-integer values are allowed. 

Also, note that the upper and lower bounds for the variables are set to negative and positive infinity respectively, as no specific bounds were mentioned in the problem description. If there are specific bounds, you can modify the `addVar` method accordingly. 

The code will output the optimal values of 'grams of fat' and 'milligrams of vitamin C' that minimize the objective function, subject to the given constraints. If no optimal solution is found, it will print a corresponding message.