For Questions $7$ to $12$:

Demand forecasts for $2021$ are as follows:

Month

Demand

Jan

$140,000$

Feb

$78,900$

Mar

$85,800$

Apr

$89,100$

May

$123,600$

Jun

$136,350$

Jul

$120,450$

Aug

$106,950$

Sep

$121,950$

Oct

$135,750$

Nov

$87,000$

Dec

$93,300$

Each worker can produce $900$ products per month and is paid $$1500$ per month.$$ Assume that at the end of last year, the company has $100$ employees working on the production line. Hiring and layoff $($firing$)$ decisions are made at the beginning of each month, and associated costs are charged at that time. It costs the company $$400$ to hire and $$800$ to lay off a worker.$$

The company incurs holding cost for the amount of ending inventory in each month, and incurs backorder cost at the end of each month for any unfilled orders. The company incurs $$2$ per month for holding one unit in inventory and $$4$ per unit backorder.

$1.$ Prepare a chase aggregate production plan. Under this plan, how many workers will be hired in the month of Apr?

$2.$ Under the chase aggregate production plan, how many workers will be fired$/$layoff in the month of November?

$3.$ Under the chase plan, what is the total cost of hiring $($NOT the overall cost$)?$

$4.$ Prepare a level aggregate plan. Under this level aggregate plan, how many workers are required in each month?

$5.$ How many workers need to be hired in the start of the planning horizon?

$6.$ Under the level production plan, what is the total cost?