Problem $4(17$ points$)$: Binary Integer Programming The brokerage firm RJ ltd$.$ 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 unit $($$$)$ Expected annual return per unit $($$$)$ Large cap common stock $120060$ Small cap common stock $3100186$ Preferred stock $7000385$ Government bonds $4500292$ Industrial bonds $6000312$ Hi$-$tech mutual funds $3800220$ Energy mutual funds $2800154$ 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. For the constraints I know there is a budget constraint, investment and non negatativty and maybe linking constraint?