Bike Friday is a small manufacturer of high$-$end folding travel bicycles. The bikes can be folded and carried in a Travelcase. The controller of Bike Friday is looking into ways to cut costs. The company purchases the Travelcases in lot sizes of $100,$ at a unit price of $$65$ plus $$4\mathrm{.}50$ for shipping expense. A lot would last a little more than one month. The purchase lead time is six to eight weeks. The controller has discovered that if the company ordered a full truckload of $500$ Travelcases at a time, the unit price will be $$50$ plus $$2\mathrm{.}50$ for shipping expense. However, Bike Friday would need a bigger storage space $(350$ square feet$)$ which was not available in$-$house. Assuming that a nearby storage space could be leased for $$400$ a month, holding cost rate of $20$ percent per unit per year, and ordering cost of $$50$ per order, determine if buying a truckload of Travelcases would have a lower total cost. $($assume we have $1000$ demand per year$).$ Please explain how carrying cost is calculated as well in full answer. Thank you