## Problem Description and Formulation

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

### Variables

* `sashimi`: number of sashimi
* `ham sandwiches`: number of ham sandwiches
* `milkshakes`: number of milkshakes
* `potatoes`: number of potatoes
* `kale salads`: number of kale salads

### Objective Function

Minimize: `9 * sashimi + 9 * ham sandwiches + 5 * milkshakes + 9 * potatoes + 8 * kale salads`

### Constraints

1. Umami index constraints:
	* `11 * ham sandwiches + 9 * potatoes >= 66`
	* `8 * sashimi + 9 * potatoes >= 40`
	* `17 * milkshakes + 9 * potatoes >= 33`
	* `11 * ham sandwiches + 17 * milkshakes + 9 * potatoes >= 57`
	* `8 * sashimi + 11 * ham sandwiches + 18 * kale salads >= 57`
	* `8 * sashimi + 17 * milkshakes + 9 * potatoes >= 57`
	* `11 * ham sandwiches + 17 * milkshakes + 18 * kale salads >= 57`
	* `17 * milkshakes + 9 * potatoes + 18 * kale salads >= 57`
	* `11 * ham sandwiches + 17 * milkshakes + 9 * potatoes >= 63`
	* `8 * sashimi + 11 * ham sandwiches + 18 * kale salads >= 63`
	* `8 * sashimi + 17 * milkshakes + 9 * potatoes >= 63`
	* `11 * ham sandwiches + 17 * milkshakes + 18 * kale salads >= 63`
	* `17 * milkshakes + 9 * potatoes + 18 * kale salads >= 63`
2. Additional constraints:
	* `-10 * sashimi + ham sandwiches >= 0`
	* `8 * ham sandwiches - 7 * kale salads >= 0`
	* `8 * sashimi + 11 * ham sandwiches + 18 * kale salads <= 150`
	* `11 * ham sandwiches + 9 * potatoes + 18 * kale salads <= 194`
	* `8 * sashimi + 9 * potatoes + 18 * kale salads <= 217`
	* `17 * milkshakes + 9 * potatoes + 18 * kale salads <= 282`
3. Integrality constraints:
	* `sashimi`, `ham sandwiches`, `milkshakes`, `potatoes`, `kale salads` are all integers

## Gurobi Code

```python
import gurobi

# Create a new Gurobi model
m = gurobi.Model()

# Define the variables
sashimi = m.addVar(name="sashimi", vtype=gurobi.GRB.INTEGER)
ham_sandwiches = m.addVar(name="ham_sandwiches", vtype=gurobi.GRB.INTEGER)
milkshakes = m.addVar(name="milkshakes", vtype=gurobi.GRB.INTEGER)
potatoes = m.addVar(name="potatoes", vtype=gurobi.GRB.INTEGER)
kale_salads = m.addVar(name="kale_salads", vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(9 * sashimi + 9 * ham_sandwiches + 5 * milkshakes + 9 * potatoes + 8 * kale_salads, gurobi.GRB.MINIMIZE)

# Define the constraints
m.addConstr(11 * ham_sandwiches + 9 * potatoes >= 66)
m.addConstr(8 * sashimi + 9 * potatoes >= 40)
m.addConstr(17 * milkshakes + 9 * potatoes >= 33)
m.addConstr(11 * ham_sandwiches + 17 * milkshakes + 9 * potatoes >= 57)
m.addConstr(8 * sashimi + 11 * ham_sandwiches + 18 * kale_salads >= 57)
m.addConstr(8 * sashimi + 17 * milkshakes + 9 * potatoes >= 57)
m.addConstr(11 * ham_sandwiches + 17 * milkshakes + 18 * kale_salads >= 57)
m.addConstr(17 * milkshakes + 9 * potatoes + 18 * kale_salads >= 57)
m.addConstr(11 * ham_sandwiches + 17 * milkshakes + 9 * potatoes >= 63)
m.addConstr(8 * sashimi + 11 * ham_sandwiches + 18 * kale_salads >= 63)
m.addConstr(8 * sashimi + 17 * milkshakes + 9 * potatoes >= 63)
m.addConstr(11 * ham_sandwiches + 17 * milkshakes + 18 * kale_salads >= 63)
m.addConstr(17 * milkshakes + 9 * potatoes + 18 * kale_salads >= 63)
m.addConstr(-10 * sashimi + ham_sandwiches >= 0)
m.addConstr(8 * ham_sandwiches - 7 * kale_salads >= 0)
m.addConstr(8 * sashimi + 11 * ham_sandwiches + 18 * kale_salads <= 150)
m.addConstr(11 * ham_sandwiches + 9 * potatoes + 18 * kale_salads <= 194)
m.addConstr(8 * sashimi + 9 * potatoes + 18 * kale_salads <= 217)
m.addConstr(17 * milkshakes + 9 * potatoes + 18 * kale_salads <= 282)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Sashimi:", sashimi.varValue)
    print("Ham Sandwiches:", ham_sandwiches.varValue)
    print("Milkshakes:", milkshakes.varValue)
    print("Potatoes:", potatoes.varValue)
    print("Kale Salads:", kale_salads.varValue)
    print("Objective function value:", m.objVal)
else:
    print("No optimal solution found.")
```