Neo EV is an electrical bus manufacturer headquartered in California. Based on historical sales data and

committed contracts, the forecast team estimates that sales in $2021$ will be as follows:

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Demand $202020203040403020202020$

Assembly of an electrical car requires a battery unit that can be manufactured by the company itself. Initially, the factory has $20$ workers on the payroll. The company can hire as many new workers as it wants in any month in $2021,$ with a hiring cost of $$4,000$ per worker $($interviewing and training$),$ whereas the company can fire workers at most once in $2021$ due to a requirement of the union contract, with a firing cost of $$15,000$ per worker $($i$.$e$.,$ severance pay$).$

Assume that, for all workers $($regardless of whether the worker is newly hired or not$),$ the monthly wage is $$5,000$ per worker on the payroll, and, on average, a worker can produce one battery unit in a month. Production cost of a battery unit is $$100,000.$

In addition, Neo EV has signed a contract with a battery supplier, BXD$,$ in Asia, which enables the former to expedite replenishment of batteries from the latter at a variable cost of $$105,000.$ BXD charges Neo EV a fixed fee $($expedite shipping and handling$)$ of $$120,000$ per order. Assume that Neo EV can decide whether to place an order or not in each month. Inventory costs of unused batteries are counted at the end of each month and have been estimated to be $$2,000$ per month per unit. Assume zero inventory initially.

The objective is to minimize the total cost, including workers$$ wage, hiring, and firing costs, production costs, inventory costs, as well as purchasing and ordering costs from the outside supplier. Build an Integer Programming spreadsheet model $($with binary variables if needed$).$ Note that the number of workers and batteries must be in integers.