Suppose you have a package weighing $9$ pounds that needs to be shipped to zone $6.$ The value of the material is $$7,000$ and the annual inventory holding rate is $20$ percent of the product value.

a$-1.$ Calculate the total shipping and transit inventory cost using the air and ground transportations.

a$-2.$ Which transportation mode $($air or ground$)$ minimizes the total shipping and transit inventory cost, and by what amount?

b$.$ How high would the inventory holding rate have to be in order to justify next$-$day air service?