Bhavika Investments, a group of financial advisors and retirement planners, has been requested to provide advice on how to invest $$200,000$ forone of its clients. The client has stipulated that the money must be put into either a stock fund or a money market fund and the annual return should be at least $$14,000.$ Other conditions related to risk have also been specified, and the following linear program was developed to help with this investment decision: Minimize risk $=12$S $+5$M subject to S $+$ M $=200,000$ total investment is $$200,0000\mathrm{.}10$S $+0\mathrm{.}05$M $14,000$ return must be at least $$14,000$M $40,000$ at least $40,000$ must bein money market fund S$,$ M $0$ where S $=$ dollars invested in stock fund M $=$ dollars invested in money market fund The QM for Windows output is shown below.$($a$)$ How much money should be invested in themoney market fund and the stock fund? What isthe total risk? $($b$)$ What is the total return? What rate of return ist his? $($c$)$ Would the solution change if the risk measurefor each dollar in the stock fund were $14$ instead of $12?($d$)$ For each additional dollar that is available, how much does the risk change? $($e$)$ Would the solution change if the amount that must be invested in the money market fund were changed from $$40,000$ to $$50,000?$