Please help $me$ check $if$ this question $is$ correct. $If$ not, please give $me$ the correct answer

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 $of960$ units. The Boilermakers

estimates the cost $to$ place $an$ order $is$ $$150,$ and the holding cost for each assembly $is$ $$25$ per

month.

$a25$ dollar monthly holding cost $to$ yearly cost$12=80$ units

Annual Ordering Cost:

Annual Ordering Cost $=$ Number $of$ Orders $$Ordering Cost $(S)$

$=12150=1,800$

Annual Holding Cost:

Average Inventory $=Q\frac{?}{?}2$

Average Inventory $=\frac{80}{2}=40$ units

Annual Holding Cost $=$ Average Inventory $$Annual Holding Cost per Unit $(H)$

Annual Holding Cost $=40300=12,000$

Total Inventory Cost $(without$ EOQ$)$:

Total Inventory Cost $=$ Annual Ordering Cost $+$ Annual Holding Cost

$=1,800+12,000=13,800$

$r^{}$

$b{Q}^{*}$ would reduce

total inventory cost. Find the optimal order quantity $Q^{*}{Q}^{*}{Q}^{*}=$

$u{?}_{(}()()2D\frac{S}{H}{)}_{?}$

Optimal Order Quantity $(Q*)$: $Q^{*}=\sqrt[\phantom{2}]{?}(2960\frac{150}{300})$

$=\sqrt[\phantom{2}]{?}960=96$ units

Order Cycle $(T)(in$ months$)$:

Order Cycle $=Q*\frac{?}{?}D12$

$T=96\frac{?}{?}96012=1\mathrm{.}2$ months

Annual Inventory Cost using EOQ:

Annual Ordering Cost:

Annual Ordering Cost $=D\frac{?}{?}Q*S$

$=\frac{960}{96}150=1,500$

Annual Holding Cost:

Annual Holding Cost $=\frac{Q^{*}}{2}H$

$=\frac{96}{2}300=14,400$

Total Inventory Cost $(using$ EOQ$)$:

Total Inventory Cost $=$ Annual Ordering Cost $+$ Annual Holding Cost

$=1,500+14,400=15,900$

larr

larr

cdarr

$=\frac{96}{4}=24$ boxes

Annual Inventory Cost:

The annual inventory cost remains the same $as$ calculated $in$ part $(b),$ which $is$ $$15,900.$