$[$Chapters $12$&$16$:$20$ points$]$ ABC is a manufacturer of precision metallic components and systems for the electric

automotive industry market. The company is a leading$-$edge supplier of engines and transmission. ABC wants to

determine the production order quantity for its engines. Annual demand for the engine is $180,000$ units. Setting up

equipment costs $$10\mathrm{.}89.$ The holding cost is $$2\mathrm{.}00$ per engine per year. The company operates its production facility $250$

days per year. ABC has the capability of producing $750$ engines per day. The cost of each engine is $$5,000.$

a$.$ Determine the production order quantity $($POQ$)$ and the number of orders. What is the total annual setup cost?

What is the total holding cost per year? Calculate the length of the production run in days. What percentage of time

will the facility be producing components? What is the setup time in minutes, based on a $$45$ per hour setup labour

cost$?$

b$.$ Using an appropriately labelled diagram, graph setup cost, holding cost, and total inventory cost, and show the

optimal production order quantity and the minimum total inventory cost.

c$.$ As part of its new JIT program, the company has signed a long$-$term contract with its customers and ABC will take

orders electronically for the engines. The setup cost will drop to $$2\mathrm{.}50,$ but the company also reassessed its holding

costs and raised them to $$2\mathrm{.}5$ per unit. Determine the new production order quantity and the number of orders

$($setups$).$ What is the total annual cost of managing the inventory with the new policy? Calculate the length of the

production run in days. What is the setup time in minutes, based on a $$45$ per hour setup labour cost with the new

policy?

d$.$ How do your answers to $1($a$)$ and $1($c$)$ provide insight into a JIT purchasing strategy? Discuss.