Given the following production plan, use a $($a$)$ chase production strategy and $($b$)$ level production strategy to compute the monthly production, ending inventory$/($backlog$)$ and workforce levels. A worker can produce $50$ units per month. Assume that the beginning inventory in January is $500$ units, and the firm desires to have $200$ units of inventory at the end of June.

$\backslash$table$[[$Month$,$Jan.,Feb.,Mar.,Apr.,May,Jun.$],[$Demand$,2000,3000,5000,6000,6000,2000],[$Production$,,,,,,],[\backslash$table$[[$Ending$],[$Inventory$]],,,,,,],[$Workforce$,,,,,,]]$

In a level production strategy, what is the inventory$/$backlog in May $($enter backlog as a negative number$)?$