The manager of the Quickie Mart convenience store $($which is open $350$ days per year$)$ sells

six cases of Duff soda each day $(2100$ cases per year$).$ Order costs are $$10\mathrm{.}00$ per order. The

lead time for an order is four days. Annual holding costs are equal to $$36$ per case.

Scenario #$1.$ The manager currently orders $50$ cases each time.

a$)$ What is the average inventory that is currently held in the store?

b$)$ Calculate the total annual ordering cost.

c$)$ Calculate the total annual holding $($carrying$)$ cost$.$

d$)$ Calculate the total annual inventory costs.

e$)$ Determine the number of orders made during the year.

f$)$ What is the re$-$order point under this scenario?

Scenario $2.$ The manager has hired you as an inventory consultant.

a$)$ Determine the optimal order quantity that should be used in order to minimize

costs. $($Round your answer to the nearest whole number$)$

b$)$ Calculate the total annual ordering cost.

c$)$ Calculate the total annual holding $($carrying$)$ cost$.$

d$)$ Calculate the total annual inventory costs. Which one of the two costs does she

save money on because of the optimal economic order quantity? Which one of the

two costs increases because of the use of the optimal economic order quantity?

e$)$ Determine the number of orders made during the year.

f$)$ What is the re$-$order point under this scenario?

g$)$ How much does she save per year in terms of total inventory costs?

h$)$ If the lead time changes to $6$ days, what is her new re$-$order point?