question in mathematical finance -for two uncorrelated assets weights of portfolio which has maximum return risk ratio are proportional to its expected return-variance ratio and what will be the weights in? assest return uncorrecelated with correclated of being f Solution Investment in the securities such as bond, debentures and shares etc.may rewarding, it is also faught with risk. As per the famous principle one cannot put all the eggs into one basket, an investor never invests his entire investments funds in one security. Investment in a portfolio can reduce risk without reducing the returns. Every investment is characterized by return and risk. The possibility of the rate of return from a security or a portfolio of securities deriving from the expected /average rate and can be measured by the standard deviation/ variance of the rate of return. One of the major benefit of portfolio was it reduce the risk of loss of capital/and or income by investing in various types of securities and over a wide range of industries. Each portfolio has its own specific risk and return .The return and risk of each portfolio can be computed mathematically based on the risk and return profiles for the constituent securities and the pair –wise correlation among them. As opposed to the expected return for a portfolio, the variance and standard deviation of a portfolio are not equal to weighted averages of the corresponding characteristics of the individual securities. The actual standard deviation for a portfolio is virtually always less than the weighted average of the standard deviations or the securities in the portfolio. The optimum portfolio of risky assets to be combined with the riskless asset. If all investors have the same expectations about asset returns and risk, each will want to hold a combined portfolio lying along the capital market line. No investor will want to hold any portfolio or risky assets other than the market Portfolio..

1. question in the link below..
https://www.dropbox.com/s/9rjiy3iz6ben4jz/2014-06-15%2019.56.49.jpg
Solution
Volume of open box = L*B*H = x*(8-2x)*(11-2x)
= (8x - 2x^2)*(11-2x)
= 88x - 16x^2 - 22x^2 + 4x^3
= 4x^3 - 38x^2 + 88x