Question $1$: $[35$pt$]($EOQ model$)$

A large bakery buys organic flour in $25-$pound bags. The bakery uses an average of $1,215$ bags a year. Preparing an order and receiving a shipment of organic flour involves a cost of $$10$ per order. Annual carrying costs are $$75$ per bag.

a$)[4$pt$]$ Determine the economic order quantity.

a$.$

b$)[3$pt$]$ What is the average number of bags on hand?

c$)[2$pt$]$ How many orders per year will there be$?$

d$)[4$pt$]$ Compute the total cost of ordering and carrying flour.

e$)[4$pt$]$ If ordering costs were to increase by $$9$ per order, how much would that affect the minimum total annual cost?

f$)[4$pt$]$ If the bakery can only order in the unit of $5$ bags, that is$,$ the bakery can only order $5,10,15$ or $...$ bags each time, what is the optimal order quantity?

g$)[4$pt$]$ If the annual carrying costs are mistakenly estimated as $$60$ per bag, what is the economic order quantity?

h$)[5$pt$]$ In this case $($as in $($g$)),$ what is the total annual cost? How much percentage does it increased from the minimum total cost?

i$)[5$pt$]$ What insight can you draw from the result of part h$?$