A property management company is building a few new houses, and has hired your engineering company as a mechanical consultant. The new houses will have a footprint of 2679 ft2, and are insulated in such a way that the houses lose ~0.13 BTU/hr per 1 ft of footprint per 1F of temperature difference between the inside and outside air. Your objective is to select a heating system which will cost the least amount of money in the long term, not just the cheapest at initial construction. Your heating options are as follows: Option 1 Electric Resistance Furnace Initial Cost: $900.00 Heating Efficiency: 100% Expected Lifetime: 20 years High Low Average The houses will be constructed in Brookings, SD, which has a historical average monthly temperature distribution as follows: Jul. Aug. Sep. 82.0 80.0 71.0 59.0 57.0 47.0 70.5 68.5 59.0 Jan. 23.0 3.0 13.0 Feb. 28.0 8.0 18.0 Mar. Apr. 39.0 21.0 30.0 Option 2 Natural Gas Furnace Initial Cost: $2,500.00 Heating Efficiency 92% Expected Lifetime: 15 Years 55.0 33.0 44.0 May. 67.0 45.0 56.0 Jun. 77.0 55.0 66.0 Option 3 Air-Source Heat Pump Initial Cost: $4,000.00 COP: 4.5 Expected Lifetime: 15 Years Nominal climate data from Brookings Regional Airport, averaged from 1981-2010. Source: U.S. Climate Data Oct. 58.0 34.0 46.0 Nov. 40.0 21.0 30.5 Dec. 26.0 7.0 16.5 Electricity for the houses will be purchased through Brookings Municipal Utilities at a rate of 0.085 $/kWh, and natural gas from Northwestern Energy at a rate of 2.60 $/MMBtu. Assume that a house will be occupied at all times by 2 people (producing -100 W each), and that the average computer, lighting, and appliance loads on any house will be 500 W, 1000 W, and 1000 W, respectively. The prospective tenants are particularly picky, and demand the inside of the houses be kept at 71F, 24 hours a day, year round. For the purposes of this analysis, you only care about the heating requirements of the house, cooling will be taken care of by one of your coworkers. Determine the following for one of the houses: (a) The annual cost to heat the houses, using each of the three options ($/year). (b) Which option is the cheapest in the long run, using simple economic analysis (assuming all costs are constant and ignoring tax, interest, the future value of money, etc)? Use two or three sentences to justify your selection. (c) What would the cost of natural gas have to be to make the natural gas furnace equally lucrative to the air-source heat pump in the long run ($/MMBtu)?