The president of Hill Enterprises, Terri Hill, projects the firm's aggregate demand requirements over the next $8$ months as follows:

Her operations manager is considering a new plan, which begins in January with $200$ units of inventory on hand. Stockout cost of lost sales is $$100$ per unit. Inventory holding

cost is $$20$ per unit per month. Ignore any idle$-$time costs. The plan is called plan $A.$

Plan A: Vary the workforce level to execute a strategy that produces the quantity demanded in the prior month. The December demand and rate of production are both

$1,600$ units per month. The cost of hiring additional workers is $$50$ per unit. The cost of laying off workers is $$75$ per unit. Evaluate this plan. $($Enter all responses as whole

numbers.$)$

Note: Both hiring and layoff costs are incurred in the month of the change. For example, going from $1,600$ in January to $1,400$ in February incurs a cost of layoff for $200$ units

in February.