## Problem Description and Formulation

The problem is an optimization problem with the goal of minimizing an objective function subject to various constraints. The variables are:

- `oranges`
- `milkshakes`
- `pickles`

The objective function to minimize is:

\[ 2.69 \times \text{oranges} + 1.69 \times \text{milkshakes} + 1.85 \times \text{pickles} \]

Subject to constraints on grams of fat (`r0`) and grams of carbohydrates (`r1`):

### Resources/Attributes

| Resource | Description          | Upper Bound | $x_0$ | $x_1$ | $x_2$ |
|----------|----------------------|-------------|-------|-------|-------|
| r0       | grams of fat         | 127         | 2     | 9     | 10    |
| r1       | grams of carbohydrates| 129         | 11    | 16    | 13    |

### Constraints

1. Fat from oranges: $2 \times \text{oranges}$
2. Carbohydrates from oranges: $11 \times \text{oranges}$
3. Fat from milkshakes: $9 \times \text{milkshakes}$
4. Carbohydrates from milkshakes: $16 \times \text{milkshakes}$
5. Fat from pickles: $10 \times \text{pickles}$
6. Carbohydrates from pickles: $13 \times \text{pickles}$

Specific constraints:

- At least 33 grams of fat from oranges and pickles: $2 \times \text{oranges} + 10 \times \text{pickles} \geq 33$
- At least 36 grams of fat from oranges and milkshakes: $2 \times \text{oranges} + 9 \times \text{milkshakes} \geq 36$
- At least 36 grams of fat from all: $2 \times \text{oranges} + 9 \times \text{milkshakes} + 10 \times \text{pickles} \geq 36$
- At least 31 grams of carbohydrates from oranges and pickles: $11 \times \text{oranges} + 13 \times \text{pickles} \geq 31$
- At least 25 grams of carbohydrates from oranges and milkshakes: $11 \times \text{oranges} + 16 \times \text{milkshakes} \geq 25$
- At least 25 grams of carbohydrates from all: $11 \times \text{oranges} + 16 \times \text{milkshakes} + 13 \times \text{pickles} \geq 25$
- $-8 \times \text{oranges} + 4 \times \text{milkshakes} \geq 0$
- $2 \times \text{milkshakes} - 9 \times \text{pickles} \geq 0$
- At most 91 grams of fat from milkshakes and pickles: $9 \times \text{milkshakes} + 10 \times \text{pickles} \leq 91$
- At most 97 grams of carbohydrates from milkshakes and pickles: $16 \times \text{milkshakes} + 13 \times \text{pickles} \leq 97$

## Gurobi Code

```python
import gurobi

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

    # Define variables
    oranges = model.addVar(lb=0, name="oranges", vtype=gurobi.GRB.CONTINUOUS)
    milkshakes = model.addVar(lb=0, name="milkshakes", vtype=gurobi.GRB.CONTINUOUS)
    pickles = model.addVar(lb=0, name="pickles", vtype=gurobi.GRB.CONTINUOUS)

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

    # Constraints
    model.addConstr(2 * oranges + 10 * pickles >= 33, name="fat_oranges_pickles")
    model.addConstr(2 * oranges + 9 * milkshakes >= 36, name="fat_oranges_milkshakes")
    model.addConstr(2 * oranges + 9 * milkshakes + 10 * pickles >= 36, name="fat_all")
    model.addConstr(11 * oranges + 13 * pickles >= 31, name="carbohydrates_oranges_pickles")
    model.addConstr(11 * oranges + 16 * milkshakes >= 25, name="carbohydrates_oranges_milkshakes")
    model.addConstr(11 * oranges + 16 * milkshakes + 13 * pickles >= 25, name="carbohydrates_all")
    model.addConstr(-8 * oranges + 4 * milkshakes >= 0, name="oranges_milkshakes_relation")
    model.addConstr(2 * milkshakes - 9 * pickles >= 0, name="milkshakes_pickles_relation")
    model.addConstr(9 * milkshakes + 10 * pickles <= 91, name="fat_milkshakes_pickles_limit")
    model.addConstr(16 * milkshakes + 13 * pickles <= 97, name="carbohydrates_milkshakes_pickles_limit")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Oranges: {oranges.varValue}")
        print(f"Milkshakes: {milkshakes.varValue}")
        print(f"Pickles: {pickles.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimization_problem()
```