Question $1(4+5+6=15$ points$)-$ EOQ model

Universal Bikes is a manufacturing company that uses gear assemblies to produce four different

models of mountain bikes. One of these gear assemblies, the "Smooth Shifter," is used for the

two most expensive models, and has an estimated annual demand of $720$ units. The Boilermakers

estimates the cost to place an order is $$150,$ and the holding cost for each assembly is $$240$ per

year.

a$)$ Currently, not knowing about EOQ, the purchasing manager places an order for the

Smooth Shifter once a month, i$.$e$.,$ twelve times per year. What is the annual total

inventory cost? $[$Rounded to $2$ decimals$]$

b$)$ You are new hire and you realize that using the optimal order quantity $Q^{**}$ would reduce

total inventory cost. Find the optimal order quantity $Q^{**}[$Rounded to whole number$].$

When using this optimal order quantity, what is the order cycle $($in months$)$ between two

orders and what is the annual total inventory cost? $[$Rounded to $2$ decimals$]$

c$)$ Suppose the supplier sells the product in boxes. Each box contains $4$ assemblies. What is

the optimal order quantity? What is the corresponding annual inventory cost?