George johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. the trust fund has two investment options: (1) a bond fund and (2) a stock fund. the projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. whatever portion of the inheritance george finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund. in addition, he wants to select a mix that will enable him to obtain a total return of at least 7.5%. formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. if required, round your answers to three decimal places. value of optimal solution is %

Your company is starting a new r& d initiative: a development of a new drug that dramatically reduces the addiction to smoking. the expert team estimates the probability of developing the drug succesfully at 60% and a chance of losing the investment of 40%. if the project is successful, your company would earn profits (after deducting the investment) of 9,000 (thousand usd). if the development is unsuccessful, the whole investment will be lost -1,000 (thousand usd). your company's risk preference is given by the expected utility function: u(x) v1000 +x, where x is the monetary outcome of a project. calculate the expected profit of the project . calculate the expected utility of the project . find the certainty equivalent of this r& d initiative . find the risk premium of this r& d initiative e is the company risk-averse, risk-loving or risk-neutral? why do you think so?