$6-68.$ Rob Roller has been in charge of inventory policy at Cyclorama, a large retail bicycle shop in Orlando, Florida. He now orders Chrome$-$Moly frames from Frameco, a local frame supplier. Cyclorama builds each bike by adding different Shimano component groups to each frame. Currently, cyclorama's annual demand for frames is $2,000$ per year. The lead time is $10$ days, and the ordering cost per order is $$50.$ The holding cost is estimated to be $25\%$ of the unit cost. Frameco offers the following discounts: $($a$)$ What are the optimal order quantity and the total inventory cost for Cyclorama given the data? $($b$)$ Rob is optimistic about future demand. If annual demand becomes $3,000$ frames, what is the impact on the optimal order quantity? $($c$)$ What is the impact if the annual demand is $4,000$ frames? $($d$)$ In general, what happens to the order quantity and total inventory cost as demand increases?