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3. Porcine Farms is trying to determine the optimal sow replacement age. Assume: (i) the age of a sow is given in the number of her lifetime litters she has weaned, (ii) the sow has a litter every 6 months, (iii) the annual discount rate is AR = 0.06 or 6 % (use m = 2 compounding periods per year), (iv) if a sow has just had her seventh litter (BOP AGE = 7) you immediately replace her with a gilt of age 0, (v) you start with a gilt with BOP age = 0, and (vi) when you replace a sow, you sell the sow and receive an amount sufficient to immediately purchase a new gilt of BOP age 0. The farm's net returns per litter for each BOP age are: BOP EOP EOP AGE AGE RETURNS 0 1 25 2 70 3 60 50 UI A J QUIA WNA 40 30 maldong 7 25 NA REPLACE a. Find the replacement age that maximizes the expected present value of one "sow- unit" in Porcine Farms. b. How might you assess the sensitivity of your answer to changes in the assumed EOP returns