In this assignment, you will develop solutions to continuous review inventory problems using the Lot Size$-$Reorder Point $($Q$,$R$)$model$.$ Show your work in Excel. Follow the instructions in each question.

Mommy's Baby Boy $($MBB$)$ is a big store selling sports equipment. A recent engineering graduate is hired for the company to help them improve their ordering policies. His first

task is to analyze a "type A$"$ product, a colorful soccer ball. MBB wants to use a lot size$-$reorder point system to control the replenishment of this popular product. Sales have an

average of $32$ units per week. The weekly demand follows a normal distribution with a standard deviation of $4.$ The store pays $$12$ per each soccer ball. Fixed replenishment

costs amount to $$15.$ The accounting department recommends using an interest rate of $10\%$ to estimate the cost of the capital, warehouse, and spoilage costs. The lead time for

an order is $1\mathrm{.}5$ months. Consider that a year has $52$ weeks and remember that it has $12$ months. Assuming that customers are willing to wait, find the right policy and the imputed

shortage cost if the company decides to have a:

a$.97\%$ Type $1$ service

b$.97\%$ Type $2$ service