The Seawall Corporation uses an injection molding machine to make a plastic$$ product, Z$39,$ after receiving firm orders from its customers. Seawall estimates that it will receive $50$ orders for Z$39$ during the coming year. Each order of Z$39$ will take $80$ hours of machine time. The annual machine capacity is $5$ comma $000$ hours.Calculate$($a$)$ the average amount of time that an order for Z$39$ will wait in line before it is processed and$($b$)$ the average manufacturing cycle time per order for Z$39.$

Seawall is considering introducing a new$$ product, Y$28.$ The company expects it will receive $25$ orders of Y$28$ in the coming year. Each order of Y$28$ will take $20$ hours of machine time. Assuming the demand for Z$39$ will not be affected by the introduction of$$ Y$28,$ calculate$($a$)$ the average waiting time for an order received and$($b$)$ the average manufacturing cycle time per order for each$$ product, if Seawall introduces Y$28.$

Seawall is debating whether it should introduce Y$28.$ The following table provides information on selling$$ prices, variable$$ costs, and inventory carrying costs for Z$39$ and$$ Y$28$:

Selling Price per Order if Average Manufacturing Cycle Time per Order Is

Product

Annual Average Number of Orders

Less Than $320$ Hours

More Than $320$ Hours

Variable Cost per Order

Inventory Carrying Cost per Order per Hour

Z$39$

$50$

$$27,000$

$$26,500$

$$15,000$

$$0\mathrm{.}75$

Y$28$

$25$

$6,400$

$6,000$

$5,000$

$0\mathrm{.}25$

Using the average manufacturing cycle times calculated in requirement$2,$ should Seawall manufacture and sell$$ Y$28?$