Ms. McBain is the proud owner of an underground oil field. Ms. McBain has only two remaining periods to live, namely periods t = 0 and t = 1. (Think of each period as being 30 years. Each person will live for 90 years, and will pass through youth (0 to 30 years old). middle age (30 to 60 years old) and old age (60 to 90 years old). Mrs. McBain is therefore 30 years old in her early years. period 0.) According to the customary law of her village which precedes the adoption of the Civil Code, Ms. McBain cannot sell her oil field because it is attached to the surface land and the latter cannot be resold. Mrs Mcbain having no heir, she will have to return her deposit to the village after her death. a) Let SO = 500 be the total amount of barrels of oil in the field. (There is no uncertainty in this problem.) A barrel of oil sells for a given unit price of $ 50 in the market, that is, po = p1 = 50. The total cost of extraction per p Period is C (Rt) = Rt2 / 20, where Rt represents the quantity extracted from barrels at t. The net profit per period is therefore it = ptrt - C (Rt). Assuming a constant discount rate r between periods, write them Ms. McBain is the proud owner of an underground oil field. Ms. McBain has only two remaining periods to live, namely periods t = 0 and t = 1. (Think of each period as being 30 years. Each person will live for 90 years, and will pass through youth (0 to 30 years old). middle age (30 to 60 years old) and old age (60 to 90 years old). Mrs. McBain is therefore 30 years old in her early years. period 0.) According to the customary law of her village which precedes the adoption of the Civil Code, Ms. McBain cannot sell her oil field because it is attached to the surface land and the latter cannot be resold. Mrs Mcbain having no heir, she will have to return her deposit to the village after her death. a) Let SO = 500 be the total amount of barrels of oil in the field. (There is no uncertainty in this problem.) A barrel of oil sells for a given unit price of $ 50 in the market, that is, po = p1 = 50. The total cost of extraction per p Period is C (Rt) = Rt2 / 20, where Rt represents the quantity extracted from barrels at t. The net profit per period is therefore it = ptrt - C (Rt). Assuming a constant discount rate r between periods, write them