Problem 4 (17 points): Binary Integer Programming The brokerage firm RJ Itd. is proposing investment guidelines for its middle-income investors. Currently, they are considering investments in several areas. Only whole units (integer) of an investment can be purchased. Investment type Cost per Expected annual unit ($) return per unit ($) Large cap common stock 1200 60 Small cap common stock 3100 186 Preferred stock 7000 385 Government bonds 4500 292 Industrial bonds 6000 312 Hi-tech mutual funds 3800 220 Energy mutual funds 2800 154 Mr. and Mrs. Green would like to invest $50,000. In addition to maximizing expected annual return, several additional restrictions on the investment portfolio have been agreed upon, to deal with diversity of portfolio and risk considerations. These restrictions are: At most one of the two common stock investment types should be made; Either both or neither of government bonds and industrial bonds should appear in the portfolio; Hi-tech mutual funds will not be in the portfolio unless preferred stock is also in the portfolio; . Energy mutual funds will not be in the portfolio unless both large cap stock and preferred stock are in the portfolio. Formulate algebraically the binary integer programming model that will help Mr. and Mrs. Green maximize the expected annual return on the investment. Define the decision variables, objective function, and constraints DO NOT Solve