$10.$ Management at the Kirby Inc. has determined the following aggregated demand schedule $($in units$).$

Month $123456789101112$

Demand $80020001,1001,5002,0003,1002,7001,5001,4001,9002,5001,500$

An employee can produce an average of $10$ units per month. Each worker on the payroll costs $$2,500$ in regular time wages per month. Undertime is paid at the same rate as regular time. In accordance to labor contract in force, Kirby Inc. does not work overtime or use subcontracting. Kerby can hire and train a new employee for $$1,500$ and lay off one for $$500.$ Inventory costs $$32$ per unit on hand at the end of each month. At present $100$ employees are on payroll, and current inventory is zero.

a$.$ Prepare a production plan using a chase strategy, relying only on hiring and layoffs. What is the total cost of this plan?

b$.$ Prepare a production plan that only uses level workforce. Layoffs, undertime, vacation, subcontracting, backorders, and stockout are not options. What is the total cost of this plan?

IMPORTANT $$ HOW TO $($Hint: Calculate the minimum number of employees required to satisfy demand for every month by maintaining end inventory at above or equals to zero.

Leftover inventory from previous month can roll over the following month. Make sure you check ending inventory at each month. End inventoryt$=$ begin inventoryt$-$demandt, while begin invt$+1=$end invt$+$productiont$+1.)$