## Problem Description and Formulation

The problem is an optimization problem where we need to maximize an objective function subject to several constraints. The objective function is to maximize \(9.11 \times \text{mg of vitamin A} + 2.55 \times \text{mg of vitamin B5} + 5.21 \times \text{g of protein} + 9.45 \times \text{g of fat}\).

The constraints are as follows:
- The digestive support index (DSI) for mg of vitamin A is 8, for mg of vitamin B5 is 7, for g of protein is 2, and for g of fat is 15.
- The total DSI from mg of vitamin A, mg of vitamin B5, and g of fat must be 31 or more.
- The total DSI from mg of vitamin A and mg of vitamin B5 must be equal to or less than 89.
- The total DSI from mg of vitamin B5 and g of protein must be equal to or less than 111.
- The total DSI from mg of vitamin A and g of fat must be equal to or less than 95.
- The total DSI from mg of vitamin B5 and g of fat should be no more than 94.
- The total DSI from mg of vitamin A, mg of vitamin B5, and g of fat must be 142 or less.
- The total DSI from all variables must be 142 or less.
- mg of vitamin A and g of fat can be non-integer, mg of vitamin B5 must be an integer, and g of protein can be non-integer.

## Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    vitamin_A = model.addVar(lb=0, name="vitamin_A", vtype=gurobi.GRB.CONTINUOUS)  # mg
    vitamin_B5 = model.addVar(lb=0, vtype=gurobi.GRB.INTEGER, name="vitamin_B5")  # mg
    protein = model.addVar(lb=0, name="protein", vtype=gurobi.GRB.CONTINUOUS)  # g
    fat = model.addVar(lb=0, name="fat", vtype=gurobi.GRB.CONTINUOUS)  # g

    # Objective function
    model.setObjective(9.11 * vitamin_A + 2.55 * vitamin_B5 + 5.21 * protein + 9.45 * fat, gurobi.GRB.MAXIMIZE)

    # Constraints
    # DSI from mg of vitamin A, mg of vitamin B5, and g of fat must be 31 or more
    model.addConstraint(8 * vitamin_A + 7 * vitamin_B5 + 15 * fat >= 31)

    # DSI from mg of vitamin A and mg of vitamin B5 must be <= 89
    model.addConstraint(8 * vitamin_A + 7 * vitamin_B5 <= 89)

    # DSI from mg of vitamin B5 and g of protein must be <= 111
    model.addConstraint(7 * vitamin_B5 + 2 * protein <= 111)

    # DSI from mg of vitamin A and g of fat must be <= 95
    model.addConstraint(8 * vitamin_A + 15 * fat <= 95)

    # DSI from mg of vitamin B5 and g of fat must be <= 94
    model.addConstraint(7 * vitamin_B5 + 15 * fat <= 94)

    # DSI from mg of vitamin A, mg of vitamin B5, and g of fat must be <= 142
    model.addConstraint(8 * vitamin_A + 7 * vitamin_B5 + 15 * fat <= 142)

    # Total DSI from all variables must be <= 142
    model.addConstraint(8 * vitamin_A + 7 * vitamin_B5 + 2 * protein + 15 * fat <= 142)

    # Upper bound for digestive support index
    model.addConstraint(8 * vitamin_A + 7 * vitamin_B5 + 2 * protein + 15 * fat <= 171)

    # Solve the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Vitamin A: {vitamin_A.varValue} mg")
        print(f"Vitamin B5: {vitamin_B5.varValue} mg")
        print(f"Protein: {protein.varValue} g")
        print(f"Fat: {fat.varValue} g")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_nutrition()
```