$\backslash$table$[[$Month$,1,2,3,4],[$Demand$,500,800,1,000,1,400],[$Month$,5,6,7,8],[$Demand$,2,000,3,000,2,700,1,500],[$Month$,9,10,11,12],[$Demand$,1,400,1,500,2,000,1,200]]$

An employee can produce an average of $10$ units per month. Each worker on the payroll costs $$2,000$ in regular$-$time wages per month. Undertime is paid at the same rate as regular time. In accordance with the labor contract in force, Kerby Corporation does not work overtime or use subcontracting. Kerby can hire and train a new employee for $$2,000$ and lay off one for $$500.$ Inventory costs $$32$ per unit on hand at the end of each month. At present, $140$ employees are on the payroll and anticipation inventory is zero.

$($a$)$ Prepare a production plan that only uses a level workforce and anticipation inventory as its supply options. Minimize the inventory left over at the end of the year. Layoffs, undertime, vacations, subcontracting, backorders, and stockouts are not options. The plan may call for a onetime adjustment of the workforce before month $1$ begins.

$($b$)$ Prepare a production plan using a chase strategy, relying only on hiring and layoffs.

$($c$)$ Prepare a mixed$-$strategy production plan that uses only a level workforce and anticipation inventory through month $7($an adjustment of the workforce may be made before month $1$ begins$)$ then switches to a chase strategy for months $8-12.$

$($d$)$ Contrast these three plans on the basis of annual costs