PROBLEM # 2 (30 points) Visiobike is a high-tech electric bicycle (e-bike) company that can be modeled as a serial two-stage supply chain, where the first stage corresponds to the manufacturing facility and the second stage is a regional distribution center. A new e-bike that integrates a carbon fiber frame with smartphone technology is currently being manufactured in the main facility and sold exclusively through the distribution center. The manufacturer makes most of the parts and performs the final assembly of the e-bike, but subcontracts the carbon fiber frames to a single supplier overseas. Each time that frames are needed, the manufacturer incurs a fixed administrative and transportation cost of K1 = $20,000 . The fixed replenishment cost for these e-bikes at the distributor is estimated to be K 2 = $800 . The unit holding cost is h, = $25 / frame / year when frames are held by the manufacturing facility and h2 =$75 / bike / year when e-bikes are held at the distribution center. The distribution center expects to sell 7,000 e-bikes per year. (a) (12 points) Compute the order quantities at the two locations and the total annual variable inventory cost by solving without inventory coordination two separate optimization problems using the basic EOQ formula.(b) (12 points) Determine the coordinated order quantities and the total annual variable inventory cost by simultaneously optimizing both stages using the exact procedure discussed in class. (c) (6 points) Compare the annual inventory costs for the inventory policies developed in parts (a) and (b). Will any of these policies result in inventory shortages? Justify your