To solve the given optimization problem using Gurobi, we need to translate the provided constraints and objective function into a format that can be used by the Gurobi solver. The objective is to minimize the cost function: $2.69 \times \text{oranges} + 1.69 \times \text{milkshakes} + 1.85 \times \text{pickles}$, subject to various constraints related to fat and carbohydrate intake from these items.

Given:
- Objective function coefficients: oranges = 2.69, milkshakes = 1.69, pickles = 1.85
- Constraints:
  - Fat content: oranges (2g), milkshakes (9g), pickles (10g)
  - Carbohydrate content: oranges (11g), milkshakes (16g), pickles (13g)
  - Minimum fat intake from various combinations of items
  - Minimum carbohydrate intake from various combinations of items
  - Linear inequality constraints involving the quantities of these items

We'll define variables for each item and then express the objective function and constraints using these variables. Since all variables are allowed to be non-integer, we will use continuous variables in Gurobi.

Here's how we can translate this problem into Gurobi code:

```python
from gurobipy import *

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

# Define the decision variables
oranges = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="oranges")
milkshakes = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milkshakes")
pickles = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="pickles")

# Objective function
m.setObjective(2.69 * oranges + 1.69 * milkshakes + 1.85 * pickles, GRB.MINIMIZE)

# Constraints
# Minimum fat intake constraints
m.addConstr(2*oranges + 10*pickles >= 33, name="min_fat_oranges_pickles")
m.addConstr(2*oranges + 9*milkshakes >= 36, name="min_fat_oranges_milkshakes")
m.addConstr(2*oranges + 9*milkshakes + 10*pickles >= 36, name="min_fat_all")

# Minimum carbohydrate intake constraints
m.addConstr(11*oranges + 13*pickles >= 31, name="min_carb_oranges_pickles")
m.addConstr(11*oranges + 16*milkshakes >= 25, name="min_carb_oranges_milkshakes")
m.addConstr(11*oranges + 16*milkshakes + 13*pickles >= 25, name="min_carb_all")

# Linear inequality constraints
m.addConstr(-8*oranges + 4*milkshakes >= 0, name="linear_ineq1")
m.addConstr(2*milkshakes - 9*pickles >= 0, name="linear_ineq2")

# Maximum fat and carbohydrate intake from milkshakes and pickles
m.addConstr(9*milkshakes + 10*pickles <= 91, name="max_fat_milkshakes_pickles")
m.addConstr(16*milkshakes + 13*pickles <= 97, name="max_carb_milkshakes_pickles")

# Upper bounds for fat and carbohydrate content (as given in the problem description)
m.addConstr(2*oranges + 9*milkshakes + 10*pickles <= 127, name="max_fat_total")
m.addConstr(11*oranges + 16*milkshakes + 13*pickles <= 129, name="max_carb_total")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Oranges: {oranges.x}")
    print(f"Milkshakes: {milkshakes.x}")
    print(f"Pickles: {pickles.x}")
else:
    print("No optimal solution found.")
```