Mr. Smith has to choose between contracts to purchase either 1000, 1200 or 1600 cattle for fattening on summer pasture. His profit depends upon on whether the pasture growing season s is good, fair or poor. The a priori subjective probability for the kind of growing season is 0.3, 0.4 and 0.3 respectively. The monetary consequences (dollar profits per animal) are s = Good s = F air s = P oor Buy 1000 18 10 8 Buy 1200 20 8 2 Buy 1600 25 6 8 If desired Mr. Smith can purchase a forecast x for the type of season for $300. The quality of the forecast (as described by likelihoods) is as follows: P (x|s) s = Good s = F air s = P oor x = Good 0.6 0.2 0.1 x = F air 0.3 0.5 0.3 x = P oor 0.1 0.3 0.6 Assuming Mr. Smith is risk neutral. a. What is the a priori optimal decision ? b. What is the maximum price Mr. Smith would be willing to pay for the forecast ? c. What is Mr. Smith optimal strategy (i.e how much cattle to buy ? should he purchase the forecast ?)