Q$1)$ 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 on hand.lost sales is lost sales is

a$)$ Plan A$.$ Produce at a constant rate $($level strategy$)$ of $1,400$ units per month, which will meet minimum demands. Then use subcontracting, with additional units at a premium price of $$75$ per unit. Evaluate this plan by computing the costs for January through August.

b$)$ Plan B$)$ Keep a stable workforce by maintaining a constant production rate equal to the average requirements and allow varying inventory levels. Beginning inventory, stockout costs, and holding costs are provided in Table.

c $)$ Plan C: Vary the workforce level $($chase strategy$)$ 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 $$5,000$ per $100$ units. The cost of laying off workers is $$7,500$ per $100$ units. Evaluate this plan.

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.