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Wondering about some changes in rock colors in her backyard and after consulting with an engineer in the neighborhood, Mrs. Lucky nds out that she has been living on an oil reserve with 30,000 barrels of recoverable oil.I The news could not come in a better time as Lucky's farming business was not going well because of bad weather and ooding in the past of couple years. Lucky consults with a few oil drilling companies to liquidify the asset as soon as she can. There are two offers on the table: 1. Given the total amount of crude oil reserve in Luckst backyard, a company will produce 6000 barrels a year for ve years and will split it by the ratio of 50-50 between Lucky and the company. 2. The second company offers that it will produce 4000 barrel a year and Lucky will pay $100,000 per year for the cost of a small drilling rig and another $150,000 per year for the cost of labour. Assume the oil reserve will be depleted completely, interest rate is 5 percent, ination rate 2 percent, and oil sells at $120 per barrel for the entire pereiod. a. Which business plan will make Lucky happier (assuming money buys happinessll? Show your work. b. Due to the recent development in fracking technology in the U.S., the oil price is expected to decline to $100 for the next two years and $90 afterward. How will this event change Lucky's decision on business plan? Show your work. c. At what prices would these two plans break-even? d. Given the original price of oil ($120], how would the present values of the plans change if interest rate increases to 7 percent? How would Lucky's choice of business plan be different? Show your work