Problem $1.(35$ points$)$ EOQ Inventory Model AURealm sells widgets and experiences a steady demand

for $1,000$ widgets per day. Each widget costs $$15$ and the delivery lead time is negligible thanks to a nearby

supplier. Handling each order costs $$25.$ Each order is delivered by a truck which costs $$75.$ The finance

manager calculated the annualized WACC $($weighted average cost of capital$)$ as $20\%.$ The company

operates $250$ business days in a year.

a$)(2$ points$)$ What is the value of the annual flow rate of AURealm, i$.$e$.,$R$?$

b$)(1\mathrm{.}5$ points$)$ What is the value of the setup cost per order for AURealm, i$.$e$.,$ K$?$

c$)(1\mathrm{.}5$ points$)$ What is the value of the holding cost per widget per year, i$.$e$.,?$

d$)(5$ points$)$ If AURealm wants to minimize its inventory management costs, how many widgets should It order every time they place an order, i$.$e$.,$ EOQ$=2$RK$/$h$?$

e$)(5$ points$)$ How many orders should AURealm place in a year, i$.$e$.,$ frequency of orders, R$/$Q$?$f$)(5$ points$)$ What is the total setup costs per year for AURealm, i$.$e$.,$ KR$/$Q$?$

g$)(5$ points$)$ How many widgets does AURealm carry on the average, i$.$e$.,$ average inventory, Q$/2?$h$)(5$ points$)$ What is the total holding costs per year for AURealm, i$.$e$.,$Q$/2?$

i$)(5$ points$)$ What is the total annual cost of managing the widget inventory for AURealm, i$.$e$.,$

$+$

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$2+?$