## Problem Description and Formulation

The problem is an optimization problem with a given objective function and constraints. The goal is to minimize the objective function subject to the provided constraints.

### Variables
- $x_0$: green beans
- $x_1$: oranges
- $x_2$: slices of pizza

### Objective Function
Minimize: $3.42x_0x_1 + 7.77x_1x_2 + 6.09x_2^2 + 3.32x_0 + 2.66x_1$

### Constraints
1. $4x_0 + 16x_1 + 20x_2 \leq 107$ (Budget constraint)
2. $5x_0 + 16x_1 + 7x_2 \leq 113$ (Tastiness rating constraint)
3. $x_0^2 + x_2^2 \geq 21$ 
4. $x_1^2 + x_2^2 \geq 23$
5. $4x_0 + 16x_1 \geq 11$
6. $4x_0 + 16x_1 + 20x_2 \geq 23$ (Total spend constraint)
7. $5x_0 + 16x_1 \geq 37$ (Tastiness rating from green beans and oranges)
8. $16x_1 + 7x_2 \geq 20$ (Tastiness rating from oranges and slices of pizza)
9. $5x_0 + 16x_1 + 7x_2 \geq 25$ (Total tastiness rating)
10. $2x_0 - 10x_2 \geq 0$
11. $5x_0 + 7x_2 \leq 68$ (Tastiness rating from green beans and slices of pizza)
12. $16^2x_1^2 + 7^2x_2^2 \leq 99$ 
13. $x_0$ is an integer
14. $x_1$ is a continuous variable
15. $x_2$ is an integer

## Gurobi Code Formulation

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define variables
x0 = m.addVar(name="green_beans", vtype=gp.GRB.INTEGER)  # green beans
x1 = m.addVar(name="oranges", vtype=gp.GRB.CONTINUOUS)  # oranges
x2 = m.addVar(name="slices_of_pizza", vtype=gp.GRB.INTEGER)  # slices of pizza

# Objective function
m.setObjective(3.42*x0*x1 + 7.77*x1*x2 + 6.09*x2**2 + 3.32*x0 + 2.66*x1, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(4*x0 + 16*x1 + 20*x2 <= 107, name="budget_constraint")
m.addConstr(5*x0 + 16*x1 + 7*x2 <= 113, name="tastiness_rating_constraint")
m.addConstr(x0**2 + x2**2 >= 21, name="green_beans_and_pizza_squared_cost")
m.addConstr(x1**2 + x2**2 >= 23, name="oranges_and_pizza_squared_cost")
m.addConstr(4*x0 + 16*x1 >= 11, name="green_beans_and_oranges_min_spend")
m.addConstr(4*x0 + 16*x1 + 20*x2 >= 23, name="total_min_spend")
m.addConstr(5*x0 + 16*x1 >= 37, name="green_beans_and_oranges_tastiness")
m.addConstr(16*x1 + 7*x2 >= 20, name="oranges_and_pizza_tastiness")
m.addConstr(5*x0 + 16*x1 + 7*x2 >= 25, name="total_tastiness_rating")
m.addConstr(2*x0 - 10*x2 >= 0, name="green_beans_and_pizza_relation")
m.addConstr(5*x0 + 7*x2 <= 68, name="green_beans_and_pizza_tastiness_limit")
m.addConstr(16**2*x1**2 + 7**2*x2**2 <= 99, name="oranges_and_pizza_tastiness_squared_limit")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Green Beans: {x0.varValue}")
    print(f"Oranges: {x1.varValue}")
    print(f"Slices of Pizza: {x2.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("The model is infeasible.")
```