Wixon Widgets has two decentralized divisions which make two different types of widgets; Premier and Popular. Because of increasing demand, each manager has been lobbying to the Headquarters for purchasing an automatic programming machine that would mechanize part of their operations. Unfortunately, these machines have huge capacity and none of the divisions of Wixon seem to have enough demand to justify purchase of these machines. The managers and the Headquarters have agreed to purchase these machines on a cost sharing agreement. At present they are considering four different options. The incremental contributions of Premier and Popular divisions for each of the four machines and the respective cost of the machines are as follows: Required 1. Which machine should the company buy, if any? (10 points) 2. If the two divisions are asked to negotiate with a 50-50 cost split, which machine would they buy? Why? Explain with numbers. (10 points) 3. How would the controller implement a decentralized decision mechanism to induce the optimal decision in a decentralized manner? Explain and verify your answer in detail. (20 Points) 4. Is this allocation fair? Why or why not? (10 points)