Betty and Bob maintain a portfolio of three stocks, A, B, and C (short positions are allowed). Each year they adjust the proportions or weightings to reflect what they hope to accomplish for the portfolio. This year the reward (rate of return) and the risk (beta) are as per Weight Return Beta A X .20 1.5 B y .05 .5 C Z .35 2.0 Portfolio 1 .15 1.2 The portfolio return is a weighted average of the returns of A,B, and C. The portfolio Beta is a weighted average of the betas of A, B, and C. Clearly each portfolio characteristic is a linear combination of the characteristics of A, B, and C. a. Write the information in the table as a system of three linear equations in three unknowns. b. Solve the system by The Row Reduction Method. Be sure to algebraically show all of your work. c. Interpret your results. If they have $100,000 assigned for use in the portfolio then what amount of money would be allocated to each stock? Be sure to indicate whether the stock position is long or short.