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: 1) 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); (1,1.)- (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). 1) (6 points) calculate mean return, 4 , 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 1>0 measures extent of risk aversion. Provide a relationship between i and o 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: 1) 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); (1,1.)- (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). 1) (6 points) calculate mean return, 4 , 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 1>0 measures extent of risk aversion. Provide a relationship between i and o 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