1. (20 points, 5 points for each part) As an elevator manager you can sell wheat to users at the following prices, Protein Content 14% or higher 13%-13.99% 12%-12.99% Price $6.20 $6.10 $6.00 It is costless for you to blend (mix) grain. What should you do to maximize revenue when you have just purchased wheat with the following attributes: i) 5,000 Bu at 14.5% and 5,000 Bu at 12.5%; ii) 3,000 Bu at 14.5% and 7,000 Bu at 12.5%. Suppose instead you face the following prices: Protein Content 14% or higher 13%-13.99% 12%-12.99% Price $6.20 $6.10 $5.90 What should you do to maximize revenue when you have just purchased wheat with the following attributes: iii) loads as in i); iv) loads as in ii)? 2. (20 points) You have $1 million to invest and you have two choices. A) Invest all at 3% rate of return over one year. B) Invest 50% in asset I providing return r, and 50% in asset 2 providing return r; where returns (including principal) per $1 invested follow the distribution (0,0) with probability 0.25(1+p): (7,0.)- (2.2,0 with probability 0.25(1 p); (0,2.2) with probability 0.25(1-P); (2.2,2.2) with probability 0.25(1+p). D) (6 points) calculate mean return, # , on the choice B) portfolio. ii) 6 points) calculate variance of returns, o, on the choice B) portfolio. iii) (6 points) Let your preferences between choices A) and B) be determined as that maximizing 4-ixo? where i>o measures extent of risk aversion. Provide a relationship between 1 and p such that you are indifferent between the two choices. iv) (2 points) comment on how the value of p affects preferences for taking the riskier choice. calculate variance of returns on the choice B) portfolio. 1. (20 points, 5 points for each part) As an elevator manager you can sell wheat to users at the following prices, Protein Content 14% or higher 13%-13.99% 12%-12.99% Price $6.20 $6.10 $6.00 It is costless for you to blend (mix) grain. What should you do to maximize revenue when you have just purchased wheat with the following attributes: i) 5,000 Bu at 14.5% and 5,000 Bu at 12.5%; ii) 3,000 Bu at 14.5% and 7,000 Bu at 12.5%. Suppose instead you face the following prices: Protein Content 14% or higher 13%-13.99% 12%-12.99% Price $6.20 $6.10 $5.90 What should you do to maximize revenue when you have just purchased wheat with the following attributes: iii) loads as in i); iv) loads as in ii)? 2. (20 points) You have $1 million to invest and you have two choices. A) Invest all at 3% rate of return over one year. B) Invest 50% in asset I providing return r, and 50% in asset 2 providing return r; where returns (including principal) per $1 invested follow the distribution (0,0) with probability 0.25(1+p): (7,0.)- (2.2,0 with probability 0.25(1 p); (0,2.2) with probability 0.25(1-P); (2.2,2.2) with probability 0.25(1+p). D) (6 points) calculate mean return, # , on the choice B) portfolio. ii) 6 points) calculate variance of returns, o, on the choice B) portfolio. iii) (6 points) Let your preferences between choices A) and B) be determined as that maximizing 4-ixo? where i>o measures extent of risk aversion. Provide a relationship between 1 and p such that you are indifferent between the two choices. iv) (2 points) comment on how the value of p affects preferences for taking the riskier choice. calculate variance of returns on the choice B) portfolio