## Problem Description and Formulation

The problem requires minimizing an objective function subject to several constraints. The objective function to be minimized is:

\[ 5x_0^2 + 9x_0x_1 + 3x_1^2 + 6x_0 + 4x_1 \]

where \(x_0\) represents the number of peanut butter sandwiches and \(x_1\) represents the number of milkshakes.

The constraints are as follows:

1. **Fiber Content**: 
   - Peanut butter sandwiches contain 0.83 grams of fiber.
   - Milkshakes contain 0.68 grams of fiber.
   - The total fiber from both must be at least 55 grams: \(0.83x_0 + 0.68x_1 \geq 55\).
   - The total fiber from both squared is also considered but directly using \(x_0^2 + x_1^2\) for fiber does not directly apply; instead, we focus on the given constraints.

2. **Tastiness Rating**:
   - Peanut butter sandwiches have a tastiness rating of 6.28.
   - Milkshakes have a tastiness rating of 10.37.
   - The total tastiness rating must be at least 18: \(6.28x_0 + 10.37x_1 \geq 18\).
   - The total tastiness rating must not exceed 73: \(6.28x_0 + 10.37x_1 \leq 73\).

3. **Other Constraints**:
   - \(3x_0 - x_1 \geq 0\).
   - The total fiber content must not exceed 100 grams: \(0.83x_0 + 0.68x_1 \leq 100\).
   - \(x_0, x_1\) can be non-integer.

## Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="peanutbutter_sandwiches", lb=0)  # Non-negative
    x1 = model.addVar(name="milkshakes", lb=0)  # Non-negative

    # Objective function
    model.setObjective(5*x0**2 + 9*x0*x1 + 3*x1**2 + 6*x0 + 4*x1, gurobi.GRB.MINIMIZE)

    # Constraints
    # Fiber content constraints
    model.addConstr(0.83*x0 + 0.68*x1 >= 55, name="min_fiber")
    model.addConstr(0.83*x0 + 0.68*x1 <= 100, name="max_fiber")

    # Tastiness rating constraints
    model.addConstr(6.28*x0 + 10.37*x1 >= 18, name="min_tastiness")
    model.addConstr(6.28*x0 + 10.37*x1 <= 73, name="max_tastiness")

    # Other constraints
    model.addConstr(3*x0 - x1 >= 0, name="ratio_constraint")

    # Solve the problem
    model.optimize()

    # Print the status
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Peanut butter sandwiches: {x0.varValue}")
        print(f"Milkshakes: {x1.varValue}")
        print(f"Objective: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The problem is infeasible.")
    else:
        print("The model status is: ", model.status)

optimize_problem()
```