To solve the given optimization problem using Gurobi, we first need to understand and translate the natural language description into a mathematical model. The objective is to maximize a linear function of variables representing milligrams of vitamin A, milligrams of vitamin B5, grams of protein, and grams of fat, subject to several constraints related to their digestive support indices.

The decision variables are:
- \(x_0\): milligrams of vitamin A
- \(x_1\): milligrams of vitamin B5
- \(x_2\): grams of protein
- \(x_3\): grams of fat

Given coefficients for the objective function and constraints:
- Objective: Maximize \(9.11x_0 + 2.55x_1 + 5.21x_2 + 9.45x_3\)
- Constraints:
  - \(8x_0 + 7x_1 + 15x_3 \geq 31\)
  - \(8x_0 + 7x_1 \leq 89\)
  - \(7x_1 + 2x_2 \leq 111\)
  - \(8x_0 + 15x_3 \leq 95\)
  - \(7x_1 + 15x_3 \leq 94\)
  - \(8x_0 + 7x_1 + 15x_3 \leq 142\)
  - \(8x_0 + 7x_1 + 2x_2 + 15x_3 \leq 142\)

Additionally, we have constraints on the nature of the variables:
- \(x_0\) can be any non-negative real number.
- \(x_1\) must be a whole number (integer).
- \(x_2\) and \(x_3\) can be any non-negative real numbers.

Here is how you could implement this in Gurobi using Python:

```python
from gurobipy import *

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

# Define variables, x0 and x1 are the first two variables
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_A")
x1 = m.addVar(vtype=GRB.INTEGER, name="milligrams_of_vitamin_B5")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="grams_of_protein")
x3 = m.addVar(vtype=GRB.CONTINUOUS, name="grams_of_fat")

# Objective function
m.setObjective(9.11*x0 + 2.55*x1 + 5.21*x2 + 9.45*x3, GRB.MAXIMIZE)

# Constraints
m.addConstr(8*x0 + 7*x1 + 15*x3 >= 31, name="digestive_support_index_1")
m.addConstr(8*x0 + 7*x1 <= 89, name="digestive_support_index_2")
m.addConstr(7*x1 + 2*x2 <= 111, name="digestive_support_index_3")
m.addConstr(8*x0 + 15*x3 <= 95, name="digestive_support_index_4")
m.addConstr(7*x1 + 15*x3 <= 94, name="digestive_support_index_5")
m.addConstr(8*x0 + 7*x1 + 15*x3 <= 142, name="digestive_support_index_6")
m.addConstr(8*x0 + 7*x1 + 2*x2 + 15*x3 <= 142, name="total_digestive_support_index")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    for v in m.getVars():
        print("%s %g" % (v.varName, v.x))
else:
    print("No optimal solution found. Status: ", m.status)
```

```python
```