## Problem Description and Formulation

The problem is an optimization problem with the goal to maximize an objective function subject to several constraints. The variables are 'cheeseburgers', 'tomatoes', and 'milkshakes'. The objective function to maximize is:

\[ 1 \times \text{cheeseburgers}^2 + 1 \times \text{cheeseburgers} \times \text{milkshakes} + 9 \times \text{tomatoes}^2 + 4 \times \text{milkshakes} \]

Subject to constraints based on the resources/attributes provided:

### Resources/Attributes

- **r0 (Calcium)**: cheeseburgers (12 mg), tomatoes (1 mg), milkshakes (11 mg), upper bound = 66 mg
- **r1 (Fiber)**: cheeseburgers (7 g), tomatoes (6 g), milkshakes (2 g), upper bound = 55 g
- **r2 (Fat)**: cheeseburgers (2 g), tomatoes (3 g), milkshakes (9 g), upper bound = 62 g

### Constraints

1. Fiber from tomatoes and milkshakes: \(6 \times \text{tomatoes} + 2 \times \text{milkshakes} \geq 15\)
2. Calcium from tomatoes and milkshakes: \(1 \times \text{tomatoes} + 11 \times \text{milkshakes} \leq 46\)
3. Calcium from cheeseburgers and tomatoes: \(12 \times \text{cheeseburgers} + 1 \times \text{tomatoes} \leq 25\)
4. Total calcium: \(12 \times \text{cheeseburgers} + 1 \times \text{tomatoes} + 11 \times \text{milkshakes} \leq 25\)
5. Fiber from cheeseburgers and tomatoes: \(7 \times \text{cheeseburgers} + 6 \times \text{tomatoes} \leq 23\)
6. Fiber from cheeseburgers and milkshakes: \(7 \times \text{cheeseburgers} + 2 \times \text{milkshakes} \leq 41\)
7. Fiber from squares: \(\text{cheeseburgers}^2 + \text{tomatoes}^2 + \text{milkshakes}^2 \leq 21\)
8. Fiber from sum: \(7 \times \text{cheeseburgers} + 6 \times \text{tomatoes} + 2 \times \text{milkshakes} \leq 21\)
9. Fat from cheeseburgers and tomatoes: \(2 \times \text{cheeseburgers} + 3 \times \text{tomatoes} \leq 44\)
10. Fat from squares of tomatoes and milkshakes: \(3^2 \times \text{tomatoes}^2 + 9^2 \times \text{milkshakes}^2 \leq 20\)
11. Fat from squares: \(2^2 \times \text{cheeseburgers}^2 + 3^2 \times \text{tomatoes}^2 + 9^2 \times \text{milkshakes}^2 \leq 28\)
12. Fat from sum: \(2 \times \text{cheeseburgers} + 3 \times \text{tomatoes} + 9 \times \text{milkshakes} \leq 28\)
13. Integrality constraints: \(\text{cheeseburgers}\) is an integer, \(\text{milkshakes}\) is an integer.

## Gurobi Code

```python
import gurobi

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

    # Define variables
    cheeseburgers = model.addVar(name="cheeseburgers", vtype=gurobi.GRB.INTEGER)
    tomatoes = model.addVar(name="tomatoes")
    milkshakes = model.addVar(name="milkshakes", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(cheeseburgers**2 + cheeseburgers * milkshakes + 9 * tomatoes**2 + 4 * milkshakes, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(6 * tomatoes + 2 * milkshakes >= 15)  # Fiber from tomatoes and milkshakes
    model.addConstr(tomatoes + 11 * milkshakes <= 46)  # Calcium from tomatoes and milkshakes
    model.addConstr(12 * cheeseburgers + tomatoes <= 25)  # Calcium from cheeseburgers and tomatoes
    model.addConstr(12 * cheeseburgers + tomatoes + 11 * milkshakes <= 25)  # Total calcium
    model.addConstr(7 * cheeseburgers + 6 * tomatoes <= 23)  # Fiber from cheeseburgers and tomatoes
    model.addConstr(7 * cheeseburgers + 2 * milkshakes <= 41)  # Fiber from cheeseburgers and milkshakes
    model.addConstr(cheeseburgers**2 + tomatoes**2 + milkshakes**2 <= 21)  # Fiber from squares
    model.addConstr(7 * cheeseburgers + 6 * tomatoes + 2 * milkshakes <= 21)  # Fiber from sum
    model.addConstr(2 * cheeseburgers + 3 * tomatoes <= 44)  # Fat from cheeseburgers and tomatoes
    model.addConstr(9 * tomatoes**2 + 81 * milkshakes**2 <= 20)  # Fat from squares of tomatoes and milkshakes
    model.addConstr(4 * cheeseburgers**2 + 9 * tomatoes**2 + 81 * milkshakes**2 <= 28)  # Fat from squares
    model.addConstr(2 * cheeseburgers + 3 * tomatoes + 9 * milkshakes <= 28)  # Fat from sum

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Cheeseburgers: ", cheeseburgers.varValue)
        print("Tomatoes: ", tomatoes.varValue)
        print("Milkshakes: ", milkshakes.varValue)
    else:
        print("Model is infeasible")

optimization_problem()
```