Q$1(100$ points$)$ A factory manufactures power drills. It is December and the projected demand for the next five months is Month Workdays Demand $($Aggregate units$)$ January $202630$ February $183850$ March $217270$ April $222790$ May $204440$ Assume normal working day has $8$ work hours. Hiring costs are $$375$ per worker and firing costs are $$650$ per worker. Holding costs are $$4$ per unit held per month. Backlog costs are $$8$ per unit help per month. Assume it takes an average of $2$ hours for one worker to assemble one product. The end inventory for December is $775,$ and the plant aims to have at most $900$ units on hand and at most $220$ units of backlog by the end of May. Assume the current work force level in December is $33$ workers.