Consider a manufacturer that produces a circuit board at a relatively stable rate of $3,000$ units per year to satisfy a relatively stable rate of $2,400$ units per year. The manufacturing setup cost is $$1,000$ per order. The unit cost of the circuit board is $$235.$ The manufacturing facility uses an annual inventory carrying rate of $18$ percent.

What is the optimal production quantity for this item?What is the maximum inventory level for the system if the optimal production quantity you found in part $($a$)$ above?

What is the optimal inventory cycle length for this item?

What are the average annual ordering and inventory holding costs for this item?

How does the optimal production quantity for this item change if the manufacturer adopts an AI$-$enabled, robotic manufacturing cell that doubles the production rate, i$.$e$.,$ to $6,000$ units per year?