2. Anaerobic methane digesters have been used for many years to reduce energy costs on farms throughout Europe and on some large farms in the United States. The digesters operate by using anaerobic bacteria to break down animal waste. During the process, which typically uses a tank heated to about 100°F (38°C) to speed the reactions, raw manure is broken down and methane is produced. The methane can then be used to generate electricity or produce heat. For a certain dairy farm with 500 cows, the cost of installing a digester is approximately $400,000. Assume that the farm uses 800,000 kilowatt-hours (kWh) of electricity each year at a cost of $0.10 per kWh. The waste from a single cow can produce 3.0 kWh of electricity each day.

(a) Assuming that the cost of electricity remains constant and the farmer starts using the manure from the cows in an anaerobic digester to produce electricity on the farm, calculate:

(i) The number of kWh of electricity that can be produced in one year

(ii) The amount of money the farmer can save in one year, NOT counting the installation cost of the digester. (You may round your answer to the nearest $1,000.)

(iii) The amount of time, in years, that it will take to recover the cost of installing an anaerobic digester on the farm. (You may round your answer to the nearest whole number of years.)

(b) Calculate the minimum number of cows the farm would need to produce 800,000 kWh of electricity per year.