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$.,h?$

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$=\sqrt[\phantom{2}]{\frac{2RK}{h}}?$

e$)(5$ points$)$ How many orders should AURealm place in a year, i$.$e$.,$ frequency of orders, $\frac{R}{Q}?$

f$)(5$ points$)$ What is the total setup costs per year for AURealm, i$.$e$.,\frac{KR}{Q}?$

g$)(5$ points$)$ How many widgets does AURealm carry on the average, i$.$e$.,$ average inventory, $\frac{Q}{2}?$

h$)(5$ points$)$ What is the total holding costs per year for AURealm, i$.$e$.,\frac{hQ}{2}?$

i$)(5$ points$)$ What is the total annual cost of managing the widget inventory for AURealm, i$.$e$.,\frac{KR}{Q}+$

$\frac{hQ}{2}+cR?$