Part $2$ Cybertruck Inventory Management $(8$ points$)$

The Laguna Hills FancyCars dealership holds a small inventory of Cybertrucks on its lot. This is a premium vehicle, with a selling price of $$100,000($for a mid$-$range trim level$).$ The dealership sells one Cybertruck each month $($i$.$e$.,$ sales are $12$ per year$).$ A special $$vehicle hauler$$ is used to transport Cybertrucks from Tesla$$s production facility to the dealership. The vehicle hauler can transport up to $7$ Cybertrucks; however, you $($as manager of the dealership$)$ are wondering whether the right replenishment order size ought to be a different quantity than $7.$

You have taken an operations management class, and have learned that it is important to balance the ordering and inventory holding costs. The FancyCars dealership owns its inventory, and purchases each Cybertruck from the Tesla factory for the wholesale price of $$70,000,$ which it then sells for $$100,000.$ Each time the dealership places an order from the Tesla factory, it incurs a fixed delivery charge of $$6000,$ which covers the cost of Tesla sending a vehicle hauler to deliver up to $7$ Cybertrucks. Assume for simplicity that there is no lead time $($i$.$e$.,$ shipments from the Tesla factory are extremely fast$)$ and there is no uncertainty in the sales volume $($i$.$e$.,$ we sell exactly one Cybertruck each month$).$ As well, the FancyCars dealership purchases its Cybertruck inventory using a line of credit which has an annual interest rate of $10\%.$ Given this information, answer the following questions.

Question $2.$a:

FancyCars estimates its inventory holding cost using its opportunity cost of capital.$$ In other words, the inventory holding cost is the financing charge $($i$.$e$.,$ interest expense$)$ that the dealership incurs from borrowing money to purchase inventory.$$ State the annual inventory holding cost per Cybertruck.

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Question $2.$b:

What is the Economic Order Quantity $($EOQ$)?($i$.$e$.,$ how many Cybertrucks should we order in each shipment?$)($Please round your answer up to a whole number$)$

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Question $2.$c:

What is the$$total annual operational$$cost$($i$.$e$.,$ the sum of ordering and holding costs$)$ of always ordering the rounded$-$up EOQ quantity? Remember: Wholesale costs of the units being purchased are never included in the ordering costs.

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Question $2.$d:

Both the newsvendor model and the EOQ model establish $$optimal order sizes.$$ Please describe the practical setting where the newsvendor setting is most appropriate, and contrast this to when the EOQ model is most appropriate.