$1.$ Weekly demand for detergent at a Carrefour store is normally distributed, with a mean of $3,000$ and a standard deviation of $1,200.$ The store manager continuously monitors detergent inventory and places a replenishment order of $10,000$ units when there are $8,000$ units in inventory. The supplier takes two and a half weeks to supply a Carrefour order.

a$)$ What CSL does the store achieve? State your answer with $3$ decimal places.

b$)$ What fill rate does the store achieve? State your answer with $3$ decimal places.

c$)$ What is the average flow time in weeks? State your answer with $2$ decimal

places.

d$)$ If the carrying cost of one unit in inventory for one year is $$1\mathrm{.}50,$ what is the

annual carrying cost based on the above inventory policy? Round your answer to the nearest integer.

$2.$ Weekly demand for paper towels at a Target store is normally distributed, with a mean of $1,700$ and a standard deviation $800.$ The supplier takes three weeks to supply a Target order, which is for a batch size of $9,000.$ Target is aiming for a fill rate of $98\mathrm{.}5\%$ and monitors its inventory continuously.

a$)$ How much safety inventory of paper towels should Target carry? Round your answer to the nearest integer.

b$)$ What should its ROP be$?$

$3.$ Weekly demand for handbags at Liverpool, a Mexican department store chain, is normally distributed with a mean of $3,600$ and a standard deviation of $2,100.$ The replenishment lead time from the supplier is $5$ weeks. Liverpool uses a periodic review policy under which it reorders handbags every $9$ weeks. It currently uses an order$-$up$-$to$-$ level of $58,000.$

a$)$ What is the average order size? Round your answer to the nearest integer. b$)$ How much safety inventory of handbags does Liverpool carry? Round your

answer to the nearest integer.

c$)$ What CSL does it achieve? Round your answer to $4$ decimal places.

d$)$ What order up to level should it use if it wants a CSL of $98\%?$ Round your

answer to the nearest integer.