Given the following information :$1.$ The demand during the lead time follows a normal distribution N$(252,100)\mathrm{.}2.$ The probability of exceeding$262$ units is about $16$ percent$\mathrm{.}3.$ The holding cost per unit per year is $$7\mathrm{.}8\mathrm{.}4.$ The average annual demand is $2835$ units$\mathrm{.}5.$ The EOQ is approximately $142$ parts$\mathrm{.}6.$ The annual inventory cost at the EOQ is approximately $$1051\mathrm{.}50\mathrm{.}7.$ The order frequency at theEOQ is approximately $20$ times per year$\mathrm{.}8.$ The unit ratio is approximately $1\mathrm{.}9.$

Please find the following:

$1.$ Using your anwer to number $8,$ what is the cost coefficient ratio of ordering yQ$*=270$ units instead of Q$*$ units?

a$\mathrm{.}1\mathrm{.}25$ b$.2\mathrm{.}75$ c$.4\mathrm{.}5$ d$.3\mathrm{.}5$

$2.$ Using your answer to the questions $3-5,$ what is the per$-$unit cost of a surplus, C$+?$

a$.$ $$0\mathrm{.}52$ b$.$ $$0\mathrm{.}19$ c$.$ $$0\mathrm{.}81$ d$.$ $$0\mathrm{.}37$

$3.$ Using the average unit cost c and revenue r along with your answer to the above question, what is the optimal service level, SL$*?$

a$.0\mathrm{.}9537$ b$.0\mathrm{.}9225$ c$.0\mathrm{.}9759$ d$.0\mathrm{.}9488$

$4.$ Considering the above question, what is the safety stock required per order at the optimal service level?

a$.18$ parts b$\mathrm{.}16$ parts c$.20$ parts d$.14$ parts

$5.$ Suppose we relaxed the service level requirement to only $0\mathrm{.}9192.$ What is the safety stock required per order at this service level?

a$.14$ parts b$.18$ parts c$.16$ parts d$.20$ parts