The government of Ivarrona faces the problem of data storage and management to make the Telemedicine Services work. Ivarrona is a country with many far-flung regions and remote islands. The data needs to be stored in regional clusters of server farms. A study commissioned by the government shows that at first, the government will need two server farms, and as Telemedicine gains acceptance in the country, more server farms will be needed. Starting with two server farms, each year, the capacity will need to grow by two server farms till it reaches a maximum of 8 server farms in four years (2 server farms in the first year, 4 in the second year, 6 in the third and 8 in the 4th year). The government does not have the capability to run server farms. It wants to give this project to a reputed data storage and management company, Dark Cloud Systems Inc. (DCS from hereon). The company offers three pricing schemes. Scheme A: Constant price of 24 dollars a year, and the government can have a maximum of 8 regional server farms. Whether the government runs 2 server farms or 8, or gradually expands to 8 regional server farms starting with 2 server farms, the company will charge a constant price of 24 dollars a year. Scheme B: A price of 4N dollars a year, where N is the number of server farms run each year for the government. Under this scheme, in the first year, the firm will charge a price of $8 (for 2 server farms), in the second year a price of 16$ (for 4 server farms), and so on till it charges a price of $32 in the fourth year for 8 server farms. Scheme C: A price of N2 (square of N) dollars a year, where N is the number of server farms run each year for the government. Under this scheme, in the first year, the firm will charge a price of $4 (for 2 server farms), in the second year a price of 16$ (for 4 server farms), and so on till it charges a price of $64 in the fourth year for 8 server farms. In addition, the company also imposes a switching cost for changing between pricing schemes. Suppose that the docs offers the government an additional incentive; if the government chooses one pricing scheme for all 4 years and does not switch. At the end of the 4th year dcs will give the government a discount of 10% of the total amount that is spent in the 4 years. What pricing scheme or single scheme should the government choose in each of the years 1 through 4? Why? The problem is only for the four year period