$5.(20$ pts$)$ A Master scheduler at Triple J$,$ has the following demand forecast for one line in his factory:

At the beginning of quarter $1,$ there are $1,000$ units in inventory. The firm has prepared the following data:

Hiring cost per employee $\backslash (=\backslash$$ $300\backslash )$

Firing cost per employee $\backslash (=\backslash$$ $500\backslash )$

Beginning workforce $\backslash (=50\backslash$mathrm$\{$employees$\}\backslash )$

Inventory carrying cost $\backslash (=\backslash$$ $3\backslash )$ per unit per quarter of average inventory

Backorder cost $\backslash (=\backslash$$ $5\backslash )$ per unit

Regular payroll $\backslash (=\backslash$$ $1,300\backslash )$ per employee per quarter

Overtime cost $=\backslash$$$3$ per unit

Each employee can produce $100$ units per quarter. If triple J produces exactly enough to meet demand each quarter, with no inventories at the end of quarters and no overtime, how much will he produce each quarter, and what is the overall cost?

b$.$ Compute a level production amount. Do not need to develop full plan just compute level product amount and number of required workers to achieve this plan.