Question $4(30$ points$)$ The following stocks are listed on the XYZ Stock Exchange: Each stock has an estimated price volatility $($variability$)$ measured as a percentage of the base price today. An investor has $\backslash (\backslash$$ $160,000\backslash )$ that can be used to purchase stocks, pay commissions and fixed fees $($if any$)$ required by the Stock Exchange. The Stock Exchange charges a commission of $\backslash (2\backslash \%\backslash )$ of the total value of the shares purchased. The Stock Exchange also charges a fixed fee $($regardless of the amount purchased$)$ of $\backslash (\backslash$$ $1000\backslash )$ for each purchased stock if fewer than $500$ shares of that stock are purchased. The $\backslash (\backslash$$ $1000\backslash )$ fixed fee $($for a stock is$)$ is waived if $500$ or more shares of a stock is purchased. The investor must purchase enough shares of various stocks to provide an annual dividend income of at least $\backslash (\backslash$$ $10,000\backslash ),$ and the average price volatility of the stocks purchased $($average calculated using the total value of shares of each stock purchased as the stock weight$)$ should not exceed $\backslash (14\backslash \%\backslash ).($a$)(20$ points$)$ Develop a suitable integer linear model to achieve this investment goal by purchasing integer quantities of each stock in a manner that minimizes the commissions and fees that are paid to the Stock Exchange. Define your decision variables clearly. $($b$)(10$ points$)$ Solve the above formulation using OpenSolver and report the solution. Submit your excel file as well. $($Hint: Optimal objective function value is $\backslash (\backslash$$ $4,059\backslash ).)$ OPEN SOLVER $$Z$$M$$LET$$R M$$S$$N$$Z$?$